A Study in Derived Algebraic Geometry: Deformations, Lie Theory and Formal Geometry
Dennis Gaitsgory, Nick Rozenblyum
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.
カテゴリー:
年:
2017
出版社:
American Mathematical Society
言語:
english
ページ:
436
ISBN 10:
1470435705
ISBN 13:
9781470435707
シリーズ:
Mathematical Surveys and Monographs
ファイル:
PDF, 2.15 MB
IPFS:
,
english, 2017