# DG Indschemes

@inproceedings{Gaitsgory2011DGI, title={DG Indschemes}, author={Dennis Gaitsgory and Nick Rozenblyum}, year={2011} }

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.

## 14 Citations

PRO-EXCISION OF ALGEBRAIC K-THEORY

- 2019

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

- Mathematics
- 2020

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

- Mathematics
- 2021

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

- Mathematics
- 2020

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

- Mathematics
- 2021

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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NOTES ON GEMETRIC LANGLANDS: QUASI-COHERENT SHEAVES ON STACKS

- 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…

Infinite-Dimensional Vector Bundles in Algebraic Geometry

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NOTES ON GEOMETRIC LANGLANDS: GENERALITIES ON DG CATEGORIES

- 2012

1.1. Continuous vs. all functors. For C1 and C2 as we consider the appropriately defined DG-category Funct(C1,C2) of k-linear functors C1 → C2, see e.g. [Dr], Sect. 16.8. Remark. We note that…

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We prove that if X is a locally complete intersection variety, then X has all the jet schemes irreducible if and only if X has canonical singularities. After embedding X in a smooth variety Y, we use…

Infinite-dimensional vector bundles

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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