A Study in Derived Algebraic Geometry – Volume II: Deformations, Lie Theory and…

A Study in Derived Algebraic GeometryVolume II: Deformations, Lie Theory and Formal Geometry\nAuthor(s): Dennis Gaitsgory, Nick Rozenblyum\nFormat: Paperback\nPublisher: American Mathematical Society, United States\nImprint: American Mathematical Society\nISBN-13: 9781470452858, 978-1470452858\nSynopsis\nDerived 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.\n\nThis volume consists of two parts. The first part introduces the notion of ind-scheme and extends the theory of.