10 citations · 41 across the 17 of their papers we have counts for
20 papers
Undecidability problems for semifree DG algebras
Ciprian Manolescu, Nick Rozenblyum
We prove that the stable tame isomorphism, quasi-isomorphism, and derived Morita equivalence problems for semifree noncommutative differential graded algebras (DGAs) are all undeci…
Applications of (higher) categorical trace II: Deligne-Lusztig theory
D. Gaitsgory, N. Rozenblyum, Y. Varshavsky
We use the formalism of the (2-category) AGCat, developed in [GRV], and the operation of higher categorical trace to (re)derive a number of results in the Deligne-Lusztig theory.
Applications of (higher) categorical trace I: the definition of AGCat
Dennis Gaitsgory, Nick Rozenblyum, Yakov Varshavsky
In this paper we record the formalism of algebro-geometric DG categories (in short AGCat) following a suggestion of V. Drinfeld. This formalism will be applied to ``real-world" pro…
Proof of the geometric Langlands conjecture IV: ambidexterity
D. Arinkin, D. Beraldo, L. Chen +5
This paper performs the following steps toward the proof of GLC in the de Rham setting: (i) We deduce GLC for G=GL_n; (ii) We prove that the Langlands functor L_G constructed in [G…
Proof of the geometric Langlands conjecture III: compatibility with parabolic induction
Justin Campbell, Lin Chen, Joakim Faergeman +4
We establish the compatibility of the Langlands functor with the operations of Eisenstein series constant term, and deduce that the Langlands functor induces an equivalence on Eise…
Symmetries of the cyclic nerve
David Ayala, Aaron Mazel-Gee, Nick Rozenblyum
We undertake a systematic study of the Hochschild homology, i.e. (the geometric realization of) the cyclic nerve, of -categories (and more generally of category-objects…
Proof of the geometric Langlands conjecture II: Kac-Moody localization and the FLE
D. Arinkin, D. Beraldo, J. Campbell +6
This paper is the second in a series of five that together prove the geometric Langlands conjecture. Our goals are two-fold: (1) Formulate and prove the Fundamental Local Equivalen…
The cyclic Deligne conjecture and Calabi-Yau structures
Christopher Brav, Nick Rozenblyum
The Deligne conjecture (many times a theorem) endows Hochschild cochains of a linear category with the structure of an -algebra, that is, of an algebra over the little 2-disks…
Connections on moduli spaces and infinitesimal Hecke modifications
Nick Rozenblyum
Let X be a proper scheme and Z a prestack over X equipped with a flat connection. We give a local-to-global description of D-modules on the prestack S(Z) of flat sections of Z. Exa…
Derived Mackey functors and -equivariant cohomology
David Ayala, Aaron Mazel-Gee, Nick Rozenblyum
We establish a novel approach to computing -equivariant cohomology for a finite group , and demonstrate it in the case that . For any commutative ring spectrum $…
Stratified noncommutative geometry
David Ayala, Aaron Mazel-Gee, Nick Rozenblyum
We introduce a theory of stratifications of noncommutative stacks (i.e. presentable stable -categories), and we prove a reconstruction theorem that expresses them in terms…
A naive approach to genuine -spectra and cyclotomic spectra
David Ayala, Aaron Mazel-Gee, Nick Rozenblyum
For any compact Lie group , we give a description of genuine -spectra in terms of the naive equivariant spectra underlying their geometric fixedpoints. We use this to give an…
The geometry of the cyclotomic trace
David Ayala, Aaron Mazel-Gee, Nick Rozenblyum
We provide a new construction of the topological cyclic homology of any spectrally-enriched -category , which affords a precise algebro-geometric interpretation…
Factorization homology of enriched -categories
David Ayala, John Francis, Aaron Mazel-Gee +1
For an arbitrary symmetric monoidal -category , we define the factorization homology of -enriched -categories over (possibly stratifie…
Gaiotto's Lagrangian subvarieties via derived symplectic geometry
Victor Ginzburg, Nick Rozenblyum
Let Bun_G be the moduli space of G-bundles on a smooth complex projective curve. Motivated by a study of boundary conditions in mirror symmetry, D. Gaiotto associated to any symple…
Factorization homology I: higher categories
David Ayala, John Francis, Nick Rozenblyum
We construct a pairing, which we call factorization homology, between framed manifolds and higher categories. The essential geometric notion is that of a vari-framing of a stratifi…
A stratified homotopy hypothesis
David Ayala, John Francis, Nick Rozenblyum
We show that conically smooth stratified spaces embed fully faithfully into -categories. This articulates a stratified generalization of the homotopy hypothesis proposed by…
Crystals and D-modules
Dennis Gaitsgory, Nick Rozenblyum
We develop the notion of crystal in the context of derived algebraic geometry, and to connect crystals to more classical objects such as D-modules.
DG Indschemes
Dennis Gaitsgory, Nick Rozenblyum
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…
Modules Over a Chiral Algebra
N. Rozenblyum
Given a chiral algebra, we study modules over an arbitrary power of a curve. We describe this category in three different ways: in terms of factorization, in terms of certain chira…