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OverviewDerived 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. Full Product DetailsAuthor: Dennis Gaitsgory , Nick RozenblyumPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.980kg ISBN: 9781470435707ISBN 10: 1470435705 Pages: 463 Publication Date: 30 September 2017 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsInf-schemes: Introduction Deformation theory Ind-schemes and inf-schemes Ind-coherent sheaves on ind-inf-schemes An application: Crystals Formal geometry: Introduction Formal moduli Lie algebras and co-commutative co-algebras Formal groups and Lie algebras Lie algebroids Infinitesimal differential geometry Bibliography Index of notations Index.ReviewsAuthor InformationDennis Gaitsgory, Harvard University, Cambridge, MA. Nick Rozenblyum, University of Chicago, IL. Tab Content 6Author Website:Countries AvailableAll regions |
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