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

Gaitsgory, Dennis; Rozenblyum, Nick

 
9781470452858: A Study in Derived Algebraic Geometry: Deformations, Lie Theory and Formal Geometry
Brossura
ISBN 10: 1470452855 ISBN 13: 9781470452858
Casa editrice: Amer Mathematical Society, 2020

Sinossi

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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Editore
Amer Mathematical Society
Data di pubblicazione
2020
Lingua
Inglese
ISBN 10 
1470452855
ISBN 13 
9781470452858
Rilegatura
Copertina flessibile
Numero di pagine
436
Contatto del produttore
non disponibile
Persona responsabile
non disponibile