Become a Readings Member to make your shopping experience even easier. Sign in or sign up for free!

Become a Readings Member. Sign in or sign up for free!

Hello Readings Member! Go to the member centre to view your orders, change your details, or view your lists, or sign out.

Hello Readings Member! Go to the member centre or sign out.

Riemann-Roch Algebra
Paperback

Riemann-Roch Algebra

$292.99
Sign in or become a Readings Member to add this title to your wishlist.

This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

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.

Read More
In Shop
Out of stock
Shipping & Delivery

$9.00 standard shipping within Australia
FREE standard shipping within Australia for orders over $100.00
Express & International shipping calculated at checkout

MORE INFO
Format
Paperback
Publisher
Springer-Verlag New York Inc.
Country
United States
Date
3 December 2010
Pages
206
ISBN
9781441930736

This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

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.

Read More
Format
Paperback
Publisher
Springer-Verlag New York Inc.
Country
United States
Date
3 December 2010
Pages
206
ISBN
9781441930736