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. 
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.Expand
Singular support of coherent sheaves and the geometric Langlands conjecture
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 derivedExpand
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 andExpand
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 asExpand
Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi–Yau 4-folds
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 aExpand
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-´Expand
    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-´ etaleExpand
      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-´ etaleExpand
        $${\mathcal {W}}$$-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 connectsExpand
        ...
        1
        2
        ...

        References

        SHOWING 1-8 OF 8 REFERENCES
        Higher Topos Theory
        This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to theExpand
        NOTES ON GEMETRIC LANGLANDS: QUASI-COHERENT SHEAVES ON STACKS
        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 theExpand
        Infinite-Dimensional Vector Bundles in Algebraic Geometry
        The goal of this work is to show that there is a reasonable algebro-geometric notion of vector bundle with infinite-dimensional locally linearly compact fibers and that these objects appear “inExpand
        NOTES ON GEOMETRIC LANGLANDS: GENERALITIES ON DG CATEGORIES
        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 thatExpand
        Jet schemes of locally complete intersection canonical singularities
        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 useExpand
        Infinite-dimensional vector bundles
        • in: Algebraic Geometry and Number Theory, Progr. Math
        • 2006
        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