Michio Kuga Kuga Varieties: Fiber Varieties Over a Symmetric Space Whose Fibers are Abelian Varieties 9787040503043

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Автор: Michio Kuga
Название: Kuga Varieties: Fiber Varieties Over a Symmetric Space Whose Fibers are Abelian Varieties
ISBN: 9787040503043
Издательство: Mare Nostrum (Eurospan)
Классификация:

Алгебра

Теория чисел

Геометрия

Алгебраическая геометрия

ISBN-10: 7040503042
Обложка/Формат: Hardback
Страницы: 172
Вес: 0.46 кг.
Дата издания: 28.02.2019
Серия: Classical topics in mathematics
Язык: English
Размер: 175 x 246 x 16
Читательская аудитория: Professional and scholarly
Ключевые слова: Algebra,Number theory,Algebraic geometry
Подзаголовок: Fiber varieties over a symmetric space whose fibers are abelian varieties
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Поставляется из: Англии
Описание: 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 Fermats Last Theorem. This book also contains one of Weils 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 Abelian Varieties, Michio Kuga