Study in derived algebraic geometry : volume II: deformations Lie theory and formal geometry - Gaitsgory, Dennis; Rozenblyum, Nick (Providence : American Mathematical Society, 2017)
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.
volume 2. Deformations, Lie theory, and formal geometry.
Includes bibliographical references and index.
Keywords: Algebraic geometry; Duality theory (Mathematics); Lie algebras; Geometry