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Homotopical algebraic geometry. II. Geometric stacks and applications

About this Title

Bertrand Toën and Gabriele Vezzosi

Publication: Memoirs of the American Mathematical Society
Publication Year 2008: Volume 193, Number 902
ISBNs: 978-0-8218-4099-3 (print); 978-1-4704-0508-3 (online)
MathSciNet review: 2394633
MSC: Primary 14A20; Secondary 18F10, 18F20, 18G55, 55P42, 55U40

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Table of Contents


  • Introduction
  • Part 1. General theory of geometric stacks
  • Introduction to Part 1
  • 1.1. Homotopical algebraic context
  • 1.2. Preliminaries on linear and commutative algebra in an HA context
  • 1.3. Geometric stacks: Basic theory
  • 1.4. Geometric stacks: Infinitesimal theory
  • Part 2. Applications
  • Introduction to Part 2
  • 2.1. Geometric $n$-stacks in algebraic geometry (after C. Simpson)
  • 2.2. Derived algebraic geometry
  • 2.3. Complicial algebraic geometry
  • 2.4. Brave new algebraic geometry