Fulton, William Lang, Serge Riemann-roch algebra 9781441930736

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Автор: Fulton, William Lang, Serge
Название: Riemann-roch algebra
ISBN: 9781441930736
Издательство: Springer
Классификация:

Алгебра

Геометрия

Алгебраическая геометрия

ISBN-10: 1441930736
Обложка/Формат: Paperback
Страницы: 216
Вес: 0.33 кг.
Дата издания: 03.12.2010
Серия: Die grundlehren der mathematischen wissenschaften
Язык: English
Издание: 1st ed. softcover of
Иллюстрации: Black & white illustrations
Размер: 158 x 235 x 17
Читательская аудитория: Professional & vocational
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: In various contexts of topology, algebraic geometry, and algebra (e.g. group representations), one meets the following situation. One has two contravariant functors K and A from a certain category to the category of rings, and a natural transformation p: K--+A of contravariant functors. The Chern character being the central exam- ple, we call the homomorphisms Px: K(X)--+ A(X) characters. Given f: X--+ Y, we denote the pull-back homomorphisms by and fA: A(Y)--+ A(X). As functors to abelian groups, K and A may also be covariant, with push-forward homomorphisms and fA: A( X)--+ A(Y). Usually these maps do not commute with the character, but there is an element r f E A(X) such that the following diagram is commutative: K(X) A(X) fK j J A K( Y) ------p;-+ A( Y) The map in the top line is p x multiplied by r f. When such commutativity holds, we say that Riemann-Roch holds for f. This type of formulation was first given by Grothendieck, extending the work of Hirzebruch to such a relative, functorial setting. Since then viii INTRODUCTION several other theorems of this Riemann-Roch type have appeared. Un- derlying most of these there is a basic structure having to do only with elementary algebra, independent of the geometry. One purpose of this monograph is to describe this algebra independently of any context, so that it can serve axiomatically as the need arises.

Riemann-roch algebra, Fulton, William Lang, Serge