Grothendieck Duality and Base Change

Brian Conrad

ISBN 10: 3540411348 / ISBN 13: 9783540411345

Published by Springer, Springer Vieweg, 2000

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783540411345

Bibliographic Details

• Title: Grothendieck Duality and Base Change
• Publisher: Springer, Springer Vieweg
• Publication Date: 2000
• Language: English
• ISBN 10: 3540411348
• ISBN 13: 9783540411345
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 233W x 155H x 17D millimeters 233 millimeters width by 155 millimeters height by 17 millimeters depth
• Weight: 472 grams

About this title

Synopsis

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.