eBook ISBN:  9781470405083 
Product Code:  MEMO/193/902.E 
List Price:  $86.00 
MAA Member Price:  $77.40 
AMS Member Price:  $51.60 
eBook ISBN:  9781470405083 
Product Code:  MEMO/193/902.E 
List Price:  $86.00 
MAA Member Price:  $77.40 
AMS Member Price:  $51.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 193; 2008; 224 ppMSC: Primary 14; 18; 55
This is the second part of a series of papers called “HAG”, devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category \(C\), and prove that this notion satisfies the expected properties.

Table of Contents

Chapters

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


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This is the second part of a series of papers called “HAG”, devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category \(C\), and prove that this notion satisfies the expected properties.

Chapters

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