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Unramified Brauer group of quotient spaces by finite groups

Andrew Kresch, Yuri Tschinkel

Abstract

We provide a general algorithm for the computation of the unramified Brauer group of quotients of rational varieties by finite groups.

Unramified Brauer group of quotient spaces by finite groups

Abstract

We provide a general algorithm for the computation of the unramified Brauer group of quotients of rational varieties by finite groups.
Paper Structure (8 sections, 16 theorems, 104 equations)

This paper contains 8 sections, 16 theorems, 104 equations.

Table of Contents

  1. Introduction
  2. Generalities
  3. Bogomolov multiplier
  4. Brauer group of the quotient stack
  5. Basic cases
  6. Grassmannians
  7. Flag varieties
  8. General approach via destackification

Key Result

Lemma 2.1

Suppose $V\to W$ is a $G$-equivariant morphism of smooth projective $G$-varieties, such that the induced homomorphism is injective (resp., an isomorphism). Then $\mathop{\mathrm{Pic}}\nolimits(W,G)\to \mathop{\mathrm{Pic}}\nolimits(V,G)$ is injective (resp., an isomorphism), and $\mathrm{Am}(W,G)$ is contained in (resp., is equal to) $\mathrm{Am}(V,G)$.

Theorems & Definitions (38)

  • Lemma 2.1
  • proof
  • Example 2.2
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Remark 3.4
  • ...and 28 more