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The small book by Shimura-Taniyama on the subject of complex multi
is a classic. It gives the results obtained by them (and some by
Weil) plication in the higher dimensional case, generalizing in a
non-trivial way the method of Deuring for elliptic curves, by
reduction mod p. Partly through the work of Shimura himself (cf.
[Sh 1] [Sh 2], and [Sh 5]), and some others (Serre, Tate, Kubota,
Ribet, Deligne etc.) it is possible today to make a more snappy and
extensive presentation of the fundamental results than was possible
in 1961. Several persons have found my lecture notes on this
subject useful to them, and so I have decided to publish this short
book to make them more widely available. Readers acquainted with
the standard theory of abelian varieties, and who wish to get
rapidly an idea of the fundamental facts of complex multi
plication, are advised to look first at the two main theorems,
Chapter 3, 6 and Chapter 4, 1, as well as the rest of Chapter 4.
The applications of Chapter 6 could also be profitably read early.
I am much indebted to N. Schappacher for a careful reading of the
manu script resulting in a number of useful suggestions. S. LANG
Contents CHAPTER 1 Analytic Complex Multiplication 4 I. Positive
Definite Involutions . . . 6 2. CM Types and Subfields. . . . . 8
3. Application to Abelian Manifolds. 4. Construction of Abelian
Manifolds with CM 14 21 5. Reflex of a CM Type . . . . .
It is possible to write endlessly on elliptic curves. (This is not
a threat.) We deal here with diophantine problems, and we lay the
foundations, especially for the theory of integral points. We
review briefly the analytic theory of the Weierstrass function, and
then deal with the arithmetic aspects of the addition formula, over
complete fields and over number fields, giving rise to the theory
of the height and its quadraticity. We apply this to integral
points, covering the inequalities of diophantine approximation both
on the multiplicative group and on the elliptic curve directly.
Thus the book splits naturally in two parts. The first part deals
with the ordinary arithmetic of the elliptic curve: The
transcendental parametrization, the p-adic parametrization, points
of finite order and the group of rational points, and the reduction
of certain diophantine problems by the theory of heights to
diophantine inequalities involving logarithms. The second part
deals with the proofs of selected inequalities, at least strong
enough to obtain the finiteness of integral points.
Diophantine problems represent some of the strongest aesthetic
attractions to algebraic geometry. They consist in giving criteria
for the existence of solutions of algebraic equations in rings and
fields, and eventually for the number of such solutions. The
fundamental ring of interest is the ring of ordinary integers Z,
and the fundamental field of interest is the field Q of rational
numbers. One discovers rapidly that to have all the technical
freedom needed in handling general problems, one must consider
rings and fields of finite type over the integers and rationals.
Furthermore, one is led to consider also finite fields, p-adic
fields (including the real and complex numbers) as representing a
localization of the problems under consideration. We shall deal
with global problems, all of which will be of a qualitative nature.
On the one hand we have curves defined over say the rational
numbers. Ifthe curve is affine one may ask for its points in Z, and
thanks to Siegel, one can classify all curves which have infinitely
many integral points. This problem is treated in Chapter VII. One
may ask also for those which have infinitely many rational points,
and for this, there is only Mordell's conjecture that if the genus
is :;;; 2, then there is only a finite number of rational points.
In the present book, we have put together the basic theory of the
units and cuspidal divisor class group in the modular function
fields, developed over the past few years. Let i) be the upper half
plane, and N a positive integer. Let r(N) be the subgroup of SL (Z)
consisting of those matrices == 1 mod N. Then r(N)\i) 2 is complex
analytic isomorphic to an affine curve YeN), whose compactifi
cation is called the modular curve X(N). The affine ring of regular
functions on yeN) over C is the integral closure of C j] in the
function field of X(N) over C. Here j is the classical modular
function. However, for arithmetic applications, one considers the
curve as defined over the cyclotomic field Q(JlN) of N-th roots of
unity, and one takes the integral closure either of Q j] or Z j],
depending on how much arithmetic one wants to throw in. The units
in these rings consist of those modular functions which have no
zeros or poles in the upper half plane. The points of X(N) which
lie at infinity, that is which do not correspond to points on the
above affine set, are called the cusps, because of the way they
look in a fundamental domain in the upper half plane. They generate
a subgroup of the divisor class group, which turns out to be
finite, and is called the cuspidal divisor class group."
This book analyzes the response of the Indonesian press to American
foreign policy during the administrations of Presidents Bush and
Obama. Situated in Southeast Asia, Indonesia is the world's fourth
most populous country and the largest Muslim nation, and as such is
a potentially vital economic and strategic partner to the US in the
21st century. Ever since Indonesian independence post World War II,
relations to the US have been marked by ups and downs. The author
argues that the way the Indonesian public perceives the world has
an impact on the national self-image that again heavily influences
national foreign affairs. For both the US and Indonesia, this is a
crucial moment in bilateral relations. This study explores
Indonesian media responses to American foreign policy by analyzing
more than 400 press articles. In the context of President Obama's
declared "pivot to Asia", both countries need to find a way to
foster better relations.
This 1999 book demonstrates a method for reading the texts of
Aristotle by revealing a continuous line of argument running from
the Physics to De Caelo. The author analyses a group of arguments
that are almost always treated in isolation from one another, and
reveals their elegance and coherence. She concludes by asking why
these arguments remain interesting even though we now believe they
are absolutely wrong and have been replaced by better ones. The
book establishes the case that we must rethink our approach to
Aristotle's physical science and Aristotelian texts, and as such
will provoke debate and stimulate new thinking amongst
philosophers, classicists, and historians of science.
'I have not seen anything quite as systematic as this material in
guiding the reader through a process for developing a valid and
reliable assessment plan. Covers all the areas one would want in
designing a system for accreditation or for other purposes' -
Martha Gage, Director, Teacher Education & Licensure, Kansas
State Department of Education 'Realistically reveals the extent of
the task of teacher certification and provides us with a structured
learning experience that should improve our abilities with this
task' - Pearl Solomon, Associate Professor, St. Thomas Aquinas
College A complete, step-by-step guide to teacher assessments that
meet national accreditation and accountability standards. Written
in a reader-friendly style for busy faculty members and school
administrators with little or no prior knowledge of statistics,
this comprehensive model is designed to create fair, valid, and
reliable assessments of teacher knowledge and skills. Evaluation
experts Judy Wilkerson and Steve Lang provide detailed guidance for
the complete five-step assessment process, making this an ideal
resource both for preservice and inservice settings, including
accreditation reviews and teacher induction programs. Offering
worksheets and activities to illustrate every step of the process,
this all-inclusive handbook covers: o Definitions, contextual
factors, and sampling o Aligning performance tasks with standards
defined by NCLB, NCATE, INTASC, and other groups o Designing and
implementing data tracking and management systems o Ensuring
psychometric integrity Valid and reliable decisions about teacher
competency are based on fair, valid, and reliable assessment
systems. Assessing Teacher Competency is the book all teacher
educators, supervisors, and mentors have been waiting for.
This book analyzes the response of the Indonesian press to American
foreign policy during the administrations of Presidents Bush and
Obama. Situated in Southeast Asia, Indonesia is the world's fourth
most populous country and the largest Muslim nation, and as such is
a potentially vital economic and strategic partner to the US in the
21st century. Ever since Indonesian independence post World War II,
relations to the US have been marked by ups and downs. The author
argues that the way the Indonesian public perceives the world has
an impact on the national self-image that again heavily influences
national foreign affairs. For both the US and Indonesia, this is a
crucial moment in bilateral relations. This study explores
Indonesian media responses to American foreign policy by analyzing
more than 400 press articles. In the context of President Obama's
declared "pivot to Asia", both countries need to find a way to
foster better relations.
"There is a vitally important link between teacher preparation and
the performance of those teachers and their students. Assessing
Teacher Competency and Assessing Teacher Dispositions provide a
strong underpinning to improve teacher competencies in both the
cognitive and affective domains in ways that we can hope will
endure post-licensure." -From the Foreword by Richard C. Kunkel
"Well researched and standards based, with activities, worksheets,
definitions, and rubrics. Addresses a topic that has been a mystery
to assessment gurus." -Marilyn K. Troupe, Director Division of
Educator Preparation, Kentucky Education Professional Standards
Board At last, a step-by-step guide for assessing teacher
dispositions that addresses national accreditation standards. While
school leaders have long sought a definitive tool for assessing
teacher affect and dispositions, a practical method for measurement
has proven elusive-until now. Assessing Teacher Dispositions
presents a conceptual framework that helps educators understand
what "appropriate dispositions" are, why it is important to measure
them, and how to implement an assessment process in their schools
and districts. This indispensable companion to Assessing Teacher
Competency introduces the authors' research-based five-step DAATS
model, combining user-friendly definitions and guiding questions
with an examination of assessment design, planning, instrument
development, decision making, and data management. Linked to
national standards for best practice set by NCATE, INTASC, and
NBPTS, the DAATS approach offers: A step-by-step implementation
sequence with worksheets and training activities Examples from
preservice and inservice settings A comprehensive assessment system
when used with the CAATS model for assessing teacher competency
(knowledge and skills) This groundbreaking text offers a
field-tested, valid, and reliable process for dispositions
assessment that is ideal for schools of education, teacher
induction programs, and preservice and inservice training.
This book is a riotous, irreverent account of the people and events
that have shaped Britain. Always getting those kings and queens
confused? Never sure what happened when? Then you need this book.
Inside you'll find rip-roaring stories of power-mad kings,
executions, invasions, high treason, global empire building, and
forbidden love - not bad for a nation of stiff upper lips! *
Revised and expanded to include the historical parliamentary
elections of 2010 and the British mission in Afghanistan *
Accompanied by access to a timeline and 'Who's Who in British
History' section on dummies.com * This new edition contains an
8-page color insert so you can see who, what and where the ensuing
historical action takes place
Kummer's work on cyclotomic fields paved the way for the
development of algebraic number theory in general by Dedekind,
Weber, Hensel, Hilbert, Takagi, Artin and others. However, the
success of this general theory has tended to obscure special facts
proved by Kummer about cyclotomic fields which lie deeper than the
general theory. For a long period in the 20th century this aspect
of Kummer's work seems to have been largely forgotten, except for a
few papers, among which are those by Pollaczek [Po], Artin-Hasse
[A-H] and Vandiver [Va]. In the mid 1950's, the theory of
cyclotomic fields was taken up again by Iwasawa and Leopoldt.
Iwasawa viewed cyclotomic fields as being analogues for number
fields of the constant field extensions of algebraic geometry, and
wrote a great sequence of papers investigating towers of cyclotomic
fields, and more generally, Galois extensions of number fields
whose Galois group is isomorphic to the additive group of p-adic
integers. Leopoldt concentrated on a fixed cyclotomic field, and
established various p-adic analogues of the classical complex
analytic class number formulas. In particular, this led him to
introduce, with Kubota, p-adic analogues of the complex L-functions
attached to cyclotomic extensions of the rationals. Finally, in the
late 1960's, Iwasawa [Iw 1 I] . made the fundamental discovery that
there was a close connection between his work on towers of
cyclotomic fields and these p-adic L-functions of Leopoldt-Kubota.
The small book by Shimura-Taniyama on the subject of complex multi
is a classic. It gives the results obtained by them (and some by
Weil) plication in the higher dimensional case, generalizing in a
non-trivial way the method of Deuring for elliptic curves, by
reduction mod p. Partly through the work of Shimura himself (cf.
[Sh 1] [Sh 2], and [Sh 5]), and some others (Serre, Tate, Kubota,
Ribet, Deligne etc.) it is possible today to make a more snappy and
extensive presentation of the fundamental results than was possible
in 1961. Several persons have found my lecture notes on this
subject useful to them, and so I have decided to publish this short
book to make them more widely available. Readers acquainted with
the standard theory of abelian varieties, and who wish to get
rapidly an idea of the fundamental facts of complex multi
plication, are advised to look first at the two main theorems,
Chapter 3, 6 and Chapter 4, 1, as well as the rest of Chapter 4.
The applications of Chapter 6 could also be profitably read early.
I am much indebted to N. Schappacher for a careful reading of the
manu script resulting in a number of useful suggestions. S. LANG
Contents CHAPTER 1 Analytic Complex Multiplication 4 I. Positive
Definite Involutions . . . 6 2. CM Types and Subfields. . . . . 8
3. Application to Abelian Manifolds. 4. Construction of Abelian
Manifolds with CM 14 21 5. Reflex of a CM Type . . . . .
ARCHIVE COpy DO NOT REMOVE The public in industrialized countries
shows a mounting concern about biological effects of electrical and
magnetic fields. As a result, experimental studies on this subject
are being published in increasing numbers throughout the world.
Prof. H. L. Konig, of the Technical University of Munich, West
Germany, a leading expert and pioneer in this field, has written an
authoritative text in a lucid style which makes the material also
accessible to lay readers. The book describes the effects of
natural as well as artificial electromagnetic energies covering the
en tire measurable frequency range from the highest frequencies,
x-rays, through microwaves, radio waves, and finally extremely low
frequency (ELF) waves. Cit ing the evidence from scientific studies
in various countries, Konig also appraises the biologic effects of
microwaves and high tension power lines, which have become
controversial issues in recent years. Other contributions to the
book have been made by Prof. Albert P. Krueger, University of
California, Berkeley, on air ionization effects and by the mete
orologist Walter Sonning on biometeorology, documenting the
influence of atmo spheric electrical currents on health and
disease. Moreover, the late Dr. Siegnot Lang, a former coworker of
Dr. Konig, has contributed to this book."
Diophantine problems represent some of the strongest aesthetic
attractions to algebraic geometry. They consist in giving criteria
for the existence of solutions of algebraic equations in rings and
fields, and eventually for the number of such solutions. The
fundamental ring of interest is the ring of ordinary integers Z,
and the fundamental field of interest is the field Q of rational
numbers. One discovers rapidly that to have all the technical
freedom needed in handling general problems, one must consider
rings and fields of finite type over the integers and rationals.
Furthermore, one is led to consider also finite fields, p-adic
fields (including the real and complex numbers) as representing a
localization of the problems under consideration. We shall deal
with global problems, all of which will be of a qualitative nature.
On the one hand we have curves defined over say the rational
numbers. Ifthe curve is affine one may ask for its points in Z, and
thanks to Siegel, one can classify all curves which have infinitely
many integral points. This problem is treated in Chapter VII. One
may ask also for those which have infinitely many rational points,
and for this, there is only Mordell's conjecture that if the genus
is :;;; 2, then there is only a finite number of rational points.
In the present book, we have put together the basic theory of the
units and cuspidal divisor class group in the modular function
fields, developed over the past few years. Let i) be the upper half
plane, and N a positive integer. Let r(N) be the subgroup of SL (Z)
consisting of those matrices == 1 mod N. Then r(N)\i) 2 is complex
analytic isomorphic to an affine curve YeN), whose compactifi
cation is called the modular curve X(N). The affine ring of regular
functions on yeN) over C is the integral closure of C j] in the
function field of X(N) over C. Here j is the classical modular
function. However, for arithmetic applications, one considers the
curve as defined over the cyclotomic field Q(JlN) of N-th roots of
unity, and one takes the integral closure either of Q j] or Z j],
depending on how much arithmetic one wants to throw in. The units
in these rings consist of those modular functions which have no
zeros or poles in the upper half plane. The points of X(N) which
lie at infinity, that is which do not correspond to points on the
above affine set, are called the cusps, because of the way they
look in a fundamental domain in the upper half plane. They generate
a subgroup of the divisor class group, which turns out to be
finite, and is called the cuspidal divisor class group."
It is possible to write endlessly on elliptic curves. (This is not
a threat.) We deal here with diophantine problems, and we lay the
foundations, especially for the theory of integral points. We
review briefly the analytic theory of the Weierstrass function, and
then deal with the arithmetic aspects of the addition formula, over
complete fields and over number fields, giving rise to the theory
of the height and its quadraticity. We apply this to integral
points, covering the inequalities of diophantine approximation both
on the multiplicative group and on the elliptic curve directly.
Thus the book splits naturally in two parts. The first part deals
with the ordinary arithmetic of the elliptic curve: The
transcendental parametrization, the p-adic parametrization, points
of finite order and the group of rational points, and the reduction
of certain diophantine problems by the theory of heights to
diophantine inequalities involving logarithms. The second part
deals with the proofs of selected inequalities, at least strong
enough to obtain the finiteness of integral points.
The rich variety of Europe's history rolled into one thrilling
account. This book takes you on a fascinating journey through the
disasters, triumphs, people, power and politics that have shaped
the Europe we know today - and you'll meet some incredible
characters along the way! From Roman relics to Renaissance, World
Wars and Eurovision, European History For Dummies packs in the
facts alongside the fun and brings the past alive. * Accompanied by
access to a value-add timeline and 'Who's Who in European History'
section on dummies.com * This new edition contains an 8-page colour
insert so you can see who, what, and where the ensuing historical
action takes place.
A belian Varieties has been out of print for a while. Since it was
written, the subject has made some great advances, and Mumford's
book giving a scheme theoretic treatment has appeared (D. Mum-
ford, Abelian Varieties, Tata Lecture Notes, Oxford University
Press, London, 1970). However, some topics covered in my book were
not covered in Mumford's; for instance, the construction of the
Picard variety, the Albanese variety, some formulas concern- ing
numerical questions, the reciprocity law for correspondences and
its application to Kummer theory, Chow's theory for the K/k-trace
and image, and others. Several people have told me they still found
a number of sections of my book useful. There- fore I thank
Springer-Verlag for the opportunity to keep the book in print. S.
LANG v FOREWORD Pour des simplifications plus subs tan- tielles, Ie
developpement futur de la geometrie algebrique ne saurait manquer
sans do ute d' en faire apparaitre. It is with considerable
pleasure that we have seen in recent years the simplifications
expected by Weil realize themselves, and it has seemed timely to
incorporate them into a new book. We treat exclusively abelian
varieties, and do not pretend to write a treatise on algebraic
groups. Hence we have summarized in a first chapter all the general
results on algebraic groups that are used in the sequel. They are
all foundational results.
Dr. Richard B. Patt, one of America's leading cancer pain experts,
teams up with science writer Susan Lang to produce a much-needed,
sensible handbook for patients and caregivers on all aspects of
cancer pain. The authors illuminate the reasons why patients are so
often undermedicated, including unfounded fears of addiction,
patients thinking they need to tough it out, time-consuming
paperwork for doctors who prescribe narcotics, and laws that fail
to distinguish between drug abuse and the legitimate employment of
narcotics. Lang and Patt demonstrate that properly medicated
patients are better able to resume active lives and marshal
strength to fight their disease - while those in chronic pain not
only suffer, but also may jeopardise their potential for recovery.
A Complete Guide to Relieving Cancer Pain and Suffering enables
cancer patients to make informed decisions about their care and
gives numerous, concrete suggestions on how patients and their
families can work most efficiently and effectively with doctors.
This volume will be of enormous value to the growing numbers of
patients, family members, and health-care professionals who are
determined to relieve needless cancer pain.
Mild depressions are so insidious that sufferers often don't seek
help. However persistent mild depression, which afflicts up to 35
million Americans, can be readily and permanently cured. This book
shows how chronic mild depression can be relieved by learning
strategies that help us to recognise negative and distorted
thinking patterns that lead to a downward spiral of pessimism. It
reveals that a combination of medication and therapy has been shown
to be the most effective treatment for mild depression, with an
impressive 85% of patients experiencing full relief. It discusses
when you should seek help from a therapist and what kinds of
therapy work best. It outlines the antidepressants that are helpful
for both mild and severe depressions, detailing each drug's
strength and weakness, and examine alternative therapies, including
stress management (meditation, relaxation, massage, biofeedback),
physical exercise, acupuncture, supplements, and other mind/body
therapies. Finally, the book provides in-depth discussions of mild
depression in children, adolescents, college students, and elderly
parents, as well as those with chronic stress. Throughout, the
authors use boxed text and charts to make the key ideas immediately
accessible and easy to use. Beating the Blues is an inspiring and
empowering book, filled with the information and encouragement you
need to turn your life around and begin to feel renewed pleasure
and joy.
An ideal double-book package covering the history of Great Britain
and the First World War. The History For Dummies collection
includes the titles British History For Dummies and First World War
For Dummies. Putting history into a perspective, British History
For Dummies is an engaging, entertaining and educational trip
through time, packing in equal parts fun and facts. Includes an 8
page colour insert. From the Somme to Gallipoli to the home front,
First World War For Dummies provides an authoritative, accessible,
and engaging introduction to the War to End All Wars. Increase your
knowledge of Great Britain and one of the most fundamental events
of the 20th Century.
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