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Grothendieck Duality and Base Change

  • Book
  • © 2000

Overview

Editors:
  1. Brian Conrad

    1. Department of Mathematics, Harvard University, Cambridge, USA
      Department of Mathematics, University of Michigan, Ann Arbor, USA

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

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About this book

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.

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-IX
    Download chapter PDF

  2. Introduction

    Pages 1-19

  3. Basic Compatibilities

    Pages 21-104

  4. Duality Foundations

    Pages 105-174

  5. Proof of Main Theorem

    Pages 175-216

  6. Examples

    Pages 217-235

  7. Back Matter

    Pages 237-296
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Editors and Affiliations

  • Department of Mathematics, Harvard University, Cambridge, USA

    Brian Conrad

  • Department of Mathematics, University of Michigan, Ann Arbor, USA

    Brian Conrad

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Bibliographic Information

  • Book Title: Grothendieck Duality and Base Change

  • Editors: Brian Conrad

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b75857

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Softcover ISBN: 978-3-540-41134-5Published: 12 December 2000

  • eBook ISBN: 978-3-540-40015-8Published: 01 July 2003

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 300

  • Topics: Algebraic Geometry, Number Theory

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