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Cohomological descent for obstructions to local-global principle

Chang Lv

Abstract

We develop a formalism of cohomological descent encoding adelic points and obstructions to local-global principle on algebraic stacks. As an application, by constructing new obstructions using the formalism, we obtain some comparison results of obstructions on some classes of algebraic stacks.

Cohomological descent for obstructions to local-global principle

Abstract

We develop a formalism of cohomological descent encoding adelic points and obstructions to local-global principle on algebraic stacks. As an application, by constructing new obstructions using the formalism, we obtain some comparison results of obstructions on some classes of algebraic stacks.
Paper Structure (6 sections, 22 theorems, 80 equations)

This paper contains 6 sections, 22 theorems, 80 equations.

Table of Contents

  1. Introduction
  2. Points and obstructions on algebraic stacks
  3. Six operation formalism and categories encoding obstructions
  4. Cohomological descent for obstructions
  5. Application to obstructions on algebraic stacks
  6. Concrete examples

Key Result

Theorem 1.1

Let ${\mathscr S\text{\upshape ch}}_{/k}'$ be a full subcategory of the category of $k$-schemes, ${\mathscr E\text{\upshape sp}}_{/k}'$ (resp. ${\mathscr C\text{\upshape hp}}_{/k}'$) be the corresponding full subcategory of the category of algebraic $k$-space (resp. sub $2$-category of the $2$-categ be a map. Then to every pair $(\text{\upshape obs}, \mathscr E)$ we may associate to a subset $X(A)

Theorems & Definitions (68)

  • Theorem 1.1: Thm. \ref{['thm_tobs']}
  • Remark 2.1
  • Definition 2.2: lv2desc
  • Remark 2.3
  • Remark 2.5
  • Proposition 2.7
  • proof
  • Lemma 3.2: lz17enhanced
  • Lemma 3.3
  • proof
  • ...and 58 more