Lectures on Algebraic Geometry I Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces
:
Günter Harder
:
H. Dietrich
:
Lectures on Algebraic Geometry I Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces
:
Vieweg+Teubner (GWV)
:
9783834895011
:
1
:
CHF 51.30
:
:
Arithmetik, Algebra
:
English
:
300
:
DRM
:
PC/MAC/eReader/Tablet
:
PDF
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own.
In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.
Prof. Dr. Günter Harder, Max-Planck-Institute for Mathematics, Bonn
Preface
5
Contents
7
Introduction
12
1 Categories, Products, Projective and Inductive Limits
14
2 Basic Concepts of Homological Algebra
24
3 Sheaves
47
4 Cohomology of Sheaves
63
5 Compact Riemann surfaces and Abelian Varieties
190
Bibliography
292
Index
295
