Grothendieck Duality and Base Change / edited by Brian Conrad.

Format:

Book

Contributor:

Conrad, Brian, 1970- editor.

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1750.

Lecture Notes in Mathematics, 0075-8434 ; 1750

Language:

English

Subjects (All):

Geometry, Algebraic.

Number theory.

Algebraic Geometry.

Number Theory.

Local Subjects:

Algebraic Geometry.

Number Theory.

Physical Description:

1 online resource (XII, 300 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2000.

System Details:

text file PDF

Summary:

Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper Cohen-Macaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory.

Contents:

Introduction

Basic compatibilities

Duality foundations

Proof of main theorom

Examples: Higher direct images. Curves

Residues and cohomology with supports

Trace map on smooth curves.

Other Format:

Printed edition:

ISBN:

9783540400158

Access Restriction:

Restricted for use by site license.