| Hardcover ISBN: | 978-7-04-050304-3 |
| Product Code: | CTM/9 |
| List Price: | $59.00 |
| AMS Member Price: | $47.20 |
| Hardcover ISBN: | 978-7-04-050304-3 |
| Product Code: | CTM/9 |
| List Price: | $59.00 |
| AMS Member Price: | $47.20 |
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Book DetailsClassical Topics in MathematicsVolume: 9; 2018; 172 ppMSC: Primary 14; 11
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.
A publication of Higher Education Press (Beijing). Exclusive rights in North America; non-exclusive outside of North America. No distribution to mainland China unless order is received through the AMS bookstore. Online bookstore rights worldwide. All standard discounts apply.
ReadershipGraduate students and research mathematicians interested in algebra, algebraic geometry, and number theory.
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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.
A publication of Higher Education Press (Beijing). Exclusive rights in North America; non-exclusive outside of North America. No distribution to mainland China unless order is received through the AMS bookstore. Online bookstore rights worldwide. All standard discounts apply.
Graduate students and research mathematicians interested in algebra, algebraic geometry, and number theory.
