Grothendieck Duality and Base Change

  • BrianĀ Conrad

Part of the Lecture Notes in Mathematics book series (LNM, volume 1750)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Pages 1-19
  3. Pages 21-104
  4. Pages 105-174
  5. Pages 175-216
  6. Pages 217-235
  7. Back Matter
    Pages 237-296

About this book

Introduction

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.

Keywords

Dualizing sheaves Grothendieck duality number theory residues trace map

Editors and affiliations

  • BrianĀ Conrad
    • 1
    • 2
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b75857
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-41134-5
  • Online ISBN 978-3-540-40015-8
  • Series Print ISSN 0075-8434
  • About this book