Grothendieck Duality and Base Change

1. Front Matter

   Pages I-IX

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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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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.

• Dualizing sheaves
• Grothendieck duality
• number theory
• residues
• trace map

• Department of Mathematics, Harvard University, Cambridge, USA

  Brian Conrad

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

  Brian Conrad

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