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Dualizing complexes for algebraic stacks

Pat Lank

Abstract

We study dualizing complexes on algebraic stacks. In particular, we establish their existence in broad generality for Deligne--Mumford stacks of characteristic zero.

Dualizing complexes for algebraic stacks

Abstract

We study dualizing complexes on algebraic stacks. In particular, we establish their existence in broad generality for Deligne--Mumford stacks of characteristic zero.
Paper Structure (10 sections, 11 theorems, 5 equations)

This paper contains 10 sections, 11 theorems, 5 equations.

Table of Contents

  1. Introduction
  2. What is known
  3. What we do
  4. Why it matters
  5. Preliminaries
  6. Categories
  7. Resolution property
  8. Functors
  9. Dualizing complexes
  10. Proofs

Key Result

Theorem 1.1

Let $f\colon \mathcal{Y}\to \mathcal{X}$ be a separated morphism of finite presentation between Deligne--Mumford $\mathbb{Q}$-stacks. Assume $\mathcal{X}$ is Noetherian and has a separated diagonal. If $K$ is a dualizing complex on $\mathcal{X}$, then $f^! K$ is a dualizing complex on $\mathcal{Y}$.

Theorems & Definitions (26)

  • Theorem 1.1
  • Corollary 1.2
  • Corollary 1.3
  • Definition 3.2
  • Remark 3.3
  • Definition 3.4
  • Remark 3.5
  • Lemma 3.6
  • proof
  • Lemma 3.7
  • ...and 16 more