Kuga varieties : fiber varieties over a symmetric space whose fibers are abeliean varieties / Michio Kuga.

Thu, 26 Nov 2020 19:43:07 +0900

Michio Kuga.. Kuga varieties : fiber varieties over a symmetric space whose fibers are abeliean varieties. Higher Education Press, 2018., Classical topics in mathematics ; 9. ISBN:7040503042; 9787040503043
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.

Kuga Varieties : fiber varieties over a symmetric space whose fibers are abeliean varieties = Kuga 簇 / Michio Kuga

Fri, 06 Mar 2026 10:03:02 +0900

Michio Kuga. Kuga Varieties : fiber varieties over a symmetric space whose fibers are abeliean varieties = Kuga 簇. Higher educatio press, 2018. ISBN:9787040503043

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Kuga varieties : fiber varieties over a symmetric space whose fibers are abeliean varieties / Michio Kuga.

Kuga Varieties : fiber varieties over a symmetric space whose fibers are abeliean varieties = Kuga 簇 / Michio Kuga