A Study in Derived Algebraic Geometry: Deformations, Lie Theory and Formal Geometry - Couverture souple

Gaitsgory, Dennis; Rozenblyum, Nick

Couverture souple

ISBN 10 : 1470452855 ISBN 13 : 9781470452858

Editeur : American Mathematical Society, 2020

Synopsis

Derived algebraic geometry is a far-reaching 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 inf-scheme, which is an infinitesimal deformation of a scheme and studies ind-coherent sheaves on such. As an application of the general theory, the six-functor formalism for D-modules in derived geometry is obtained.

This volume consists of two parts. The first part introduces the notion of ind-scheme and extends the theory of ind-coherent sheaves to inf-schemes, obtaining the theory of D-modules as an application. The second part establishes the equivalence between formal Lie group(oids) and Lie algebr(oids) in the category of ind-coherent 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.

A propos du livre

À propos de l?auteur

Dennis Gaitsgory, Harvard University, Cambridge, MA.

Nick Rozenblyum, University of Chicago, IL.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2020
• Langue: anglais
• ISBN 10: 1470452855
• ISBN 13: 9781470452858
• Reliure: Broché
• Nombre de pages: 436
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible