# DG Indschemes

@inproceedings{Gaitsgory2011DGI,
title={DG Indschemes},
author={Dennis Gaitsgory and Nick Rozenblyum},
year={2011}
}
• Published 8 August 2011
• Mathematics
We develop the notion of indscheme in the context of derived algebraic geometry, and study the categories of quasi-coherent sheaves and ind-coherent sheaves on indschemes. The main results concern the relation between classical and derived indschemes and the notion of formal smoothness.
PRO-EXCISION OF ALGEBRAIC K-THEORY
This is an expository article on the pro-excision theorem of algebraic K-theory for abstract blow-up squares, due to Kerz-Strunk-Tamme [KST18].
Homological methods in semi-infinite contexts
Actions of algebraic groups on DG categories provide a convenient, unifying framework in some parts of geometric representation theory, especially the representation theory of reductive Lie algebras.
Singular support of coherent sheaves and the geometric Langlands conjecture
• Mathematics
• 2012
We define the notion of singular support of a coherent sheaf on a quasi-smooth-derived scheme or Artin stack, where “quasi-smooth” means that it is a locally complete intersection in the derived
Faisceaux caract\'eres sur les espaces de lacets d'alg\`ebres de Lie
We establish several foundational results regarding the Grothendieck-Springer affine fibration. More precisely, we prove some constructibility results on the affine Grothendieck-Springer sheaf and
Equivariant localization and completion in cyclic homology and derived loop spaces
We prove an equivariant localization theorem over an algebraically closed field of characteristic zero for smooth quotient stacks by reductive groups $X/G$ in the setting of derived loop spaces as
Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi–Yau 4-folds
• Mathematics, Physics
• 2018
Abstract Suppose ( X , Ω , g ) is a compact Spin ( 7 ) -manifold, e.g. a Riemannian 8-manifold with holonomy Spin ( 7 ) , or a Calabi–Yau 4-fold. Let G be U ( m ) or SU ( m ) , and P → X be a
Pro-´ Etale Cohomology
0965 Contents 1. Introduction 1 2. Some topology 2 3. Local isomorphisms 4 4. Ind-Zariski algebra 6 5. Constructing w-local affine schemes 6 6. Identifying local rings versus ind-Zariski 10 7. Ind-´
Pro-´ Etale Cohomology
Contents 1. Introduction 1 2. Some topology 2 3. Local isomorphisms 4 4. Ind-Zariski algebra 6 5. Constructing w-local affine schemes 6 6. Identifying local rings versus ind-Zariski 10 7. Ind-´ etale
Pro-´ Etale Cohomology
Contents 1. Introduction 1 2. Some topology 2 3. Local isomorphisms 4 4. Ind-Zariski algebra 6 5. Constructing w-local affine schemes 6 6. Identifying local rings versus ind-Zariski 10 7. Ind-´ etale
$${\mathcal {W}}$$-algebras and Whittaker categories
This article is concerned with Whittaker models in geometric representation theory, and gives applications to the study of affine $${\mathcal {W}}$$ -algebras. The main new innovation connects

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• 2011
Like [GL:Stacks], this paper isn't really a paper either. I will try to record the basic facts and definitions regarding quasi-coherent sheaves on stacks in the DG setting. The vast majority of the
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A study in derived algebraic geometry, in preparation, preliminary version will gradually become available at http://www
• A study in derived algebraic geometry, in preparation, preliminary version will gradually become available at http://www