ENGLISH

Kuga Varieties: Fiber Varieties over a Symmetric Space Whose Fibers Are Abeliean Varieties (Classical Topics in Mathematics)

By Michio Kuga

Book information

Publisher
American Mathematical Society/Higher Education Press
Year
2019
ISBN
7040503042, 9787040503043
Language
english
Format
DJVU
Filesize
1 MB (1455543 bytes)
Series
Classical Topics in Mathematics (Book 9)
Edition
1
Pages
172\175
Time added
2020-07-27 12:19:47

Description

Kuga varieties are fiber varieties over symmetric spaces whose fibers are abelian varieties and have played an important role in the theory of Shimura varieties and number theory. This book is the first systematic exposition of these varieties and was written by their creators. It contains four chapters. Chapter 1 gives a detailed generalization to vector valued harmonic forms. These results are applied to construct Kuga varieties in Chapter 2 and to understand their cohomology groups. Chapter 3 studies Hecke operators, which are the most basic operators in modular forms. All the previous results are applied in Chapter 4 to prove the modularity property of certain Kuga varieties. Note that the modularity property of elliptic curves is the key ingredient of Wiles' proof of Fermat's Last Theorem. This book also contains one of Weil's letters and a paper by Satake which are relevant to the topic of the book.

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