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Softcover ISBN:  9781470452858 
Product Code:  SURV/221.2.S 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470440879 
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MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470452858 
eBook ISBN:  9781470440879 
Product Code:  SURV/221.2.S.B 
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MAA Member Price:  $228.60 $172.35 
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Book DetailsMathematical Surveys and MonographsVolume: 221; 2017; 436 ppMSC: Primary 14; 18
Derived algebraic geometry is a farreaching generalization of algebraic geometry. It has found numerous applications in other parts of mathematics, most prominently in representation theory. This volume develops deformation theory, Lie theory and the theory of algebroids in the context of derived algebraic geometry. To that end, it introduces the notion of infscheme, which is an infinitesimal deformation of a scheme and studies indcoherent sheaves on such. As an application of the general theory, the sixfunctor formalism for Dmodules in derived geometry is obtained.
This volume consists of two parts. The first part introduces the notion of indscheme and extends the theory of indcoherent sheaves to infschemes, obtaining the theory of Dmodules as an application. The second part establishes the equivalence between formal Lie group(oids) and Lie algebr(oids) in the category of indcoherent sheaves. This equivalence gives a vast generalization of the equivalence between Lie algebras and formal moduli problems. This theory is applied to study natural filtrations in formal derived geometry generalizing the Hodge filtration.
ReadershipGraduate students and researchers interested in new trends in algebraic geometry and representation theory.
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Table of Contents

Infschemes

Introduction

Deformation theory

Indschemes and infschemes

Indcoherent sheaves on indinfschemes

An application: Crystals

Formal geometry

Introduction

Formal moduli

Lie algebras and cocommutative coalgebras

Formal groups and Lie algebras

Lie algebroids

Infinitesimal differential geometry


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Derived algebraic geometry is a farreaching generalization of algebraic geometry. It has found numerous applications in other parts of mathematics, most prominently in representation theory. This volume develops deformation theory, Lie theory and the theory of algebroids in the context of derived algebraic geometry. To that end, it introduces the notion of infscheme, which is an infinitesimal deformation of a scheme and studies indcoherent sheaves on such. As an application of the general theory, the sixfunctor formalism for Dmodules in derived geometry is obtained.
This volume consists of two parts. The first part introduces the notion of indscheme and extends the theory of indcoherent sheaves to infschemes, obtaining the theory of Dmodules as an application. The second part establishes the equivalence between formal Lie group(oids) and Lie algebr(oids) in the category of indcoherent sheaves. This equivalence gives a vast generalization of the equivalence between Lie algebras and formal moduli problems. This theory is applied to study natural filtrations in formal derived geometry generalizing the Hodge filtration.
Graduate students and researchers interested in new trends in algebraic geometry and representation theory.

Infschemes

Introduction

Deformation theory

Indschemes and infschemes

Indcoherent sheaves on indinfschemes

An application: Crystals

Formal geometry

Introduction

Formal moduli

Lie algebras and cocommutative coalgebras

Formal groups and Lie algebras

Lie algebroids

Infinitesimal differential geometry