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Books > Science & Mathematics > Mathematics > Algebra
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Complex Multiplication and Lifting Problems (Hardcover)
Loot Price: R3,330
Discovery Miles 33 300
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Complex Multiplication and Lifting Problems (Hardcover)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 17 working days
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Abelian varieties with complex multiplication lie at the origins of
class field theory, and they play a central role in the
contemporary theory of Shimura varieties. They are special in
characteristic 0 and ubiquitous over finite fields. This book
explores the relationship between such abelian varieties over
finite fields and over arithmetically interesting fields of
characteristic 0 via the study of several natural CM lifting
problems which had previously been solved only in special cases. In
addition to giving complete solutions to such questions, the
authors provide numerous examples to illustrate the general theory
and present a detailed treatment of many fundamental results and
concepts in the arithmetic of abelian varieties, such as the Main
Theorem of Complex Multiplication and its generalisations, the
finer aspects of Tate's work on abelian varieties over finite
fields, and deformation theory. This book provides an ideal
illustration of how modern techniques in arithmetic geometry (such
as descent theory, crystalline methods, and group schemes) can be
fruitfully combined with class field theory to answer concrete
questions about abelian varieties. It will be a useful reference
for researchers and advanced graduate students at the interface of
number theory and algebraic geometry.
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