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Conjectures in Arithmetic Algebraic Geometry - A Survey (Hardcover, Softcover Reprint Of The Original 1st Ed. 1992)
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Conjectures in Arithmetic Algebraic Geometry - A Survey (Hardcover, Softcover Reprint Of The Original 1st Ed. 1992)
Series: Aspects of Mathematics S., v.18
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In this expository paper we sketch some interrelations between
several famous conjectures in number theory and algebraic geometry
that have intrigued mathematicians for a long period of time.
Starting from Fermat's Last Theorem one is naturally led to intro
duce L-functions, the main motivation being the calculation of
class numbers. In particular, Kummer showed that the class numbers
of cyclotomic fields playa decisive role in the corroboration of
Fermat's Last Theorem for a large class of exponents. Before
Kummer, Dirich let had already successfully applied his L-functions
to the proof of the theorem on arithmetic progressions. Another
prominent appearance of an L-function is Riemann's paper where the
now famous Riemann Hypothesis was stated. In short, nineteenth
century number theory showed that much, if not all, of number
theory is reflected by proper ties of L-functions. Twentieth
century number theory, class field theory and algebraic geometry
only strengthen the nineteenth century number theorists's view. We
just mention the work of E. Heeke, E. Artin, A. Weil and A.
Grothendieck with his collaborators. Heeke generalized Dirichlet's
L-functions to obtain results on the distribution of primes in
number fields. Artin introduced his L-functions as a non-abelian
generaliza tion of Dirichlet's L-functions with a generalization of
class field the ory to non-abelian Galois extensions of number
fields in mind. Weil introduced his zeta-function for varieties
over finite fields in relation to a problem in number theory."
General
Imprint: |
Friedrich Vieweg & Sohn Verlagsgesellschaft Mbh
|
Country of origin: |
Germany |
Series: |
Aspects of Mathematics S., v.18 |
Release date: |
1992 |
First published: |
1992 |
Authors: |
Wilfred W.J. Hulsbergen
|
Dimensions: |
230 x 155 x 13mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
244 |
Edition: |
Softcover Reprint Of The Original 1st Ed. 1992 |
ISBN-13: |
978-3-528-06433-4 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
Algebraic geometry
|
LSN: |
3-528-06433-1 |
Barcode: |
9783528064334 |
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