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A Study in Derived Algebraic Geometry, Part 1: Volume I: Correspondences and Duality

- D. Gaitsgory, N. Rozenblyum
- Mathematics
- 6 July 2017

Factorization homology I: higher categories

- David Ayala, J. Francis, N. Rozenblyum
- Mathematics
- 15 April 2015

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 stratified manifold, which… Expand

Crystals and D-modules

- D. Gaitsgory, N. Rozenblyum
- Mathematics
- 9 November 2011

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.

A naive approach to genuine $G$-spectra and cyclotomic spectra

- David Ayala, Aaron Mazel-Gee, N. Rozenblyum
- Mathematics
- 17 October 2017

For any compact Lie group $G$, we give a description of genuine $G$-spectra in terms of the naive equivariant spectra underlying their geometric fixedpoints. We use this to give an analogous… Expand

A stratified homotopy hypothesis

- David Ayala, J. Francis, N. Rozenblyum
- Mathematics
- 5 February 2015

We show that conically smooth stratified spaces embed fully faithfully into $\infty$-categories. This articulates a stratified generalization of the homotopy hypothesis proposed by Grothendieck. As… Expand

Gaiotto’s Lagrangian Subvarieties via Derived Symplectic Geometry

- V. Ginzburg, N. Rozenblyum
- Mathematics, Physics
- 24 March 2017

Let BunG be the moduli space of G-bundles on a smooth complex projective curve. Motivated by a study of boundary conditions in mirror symmetry, Gaiotto (2016) associated to any symplectic… Expand

DG Indschemes

- D. Gaitsgory, N. Rozenblyum
- Mathematics
- 8 August 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… Expand

FACTORIZATION HOMOLOGY OF ENRICHED ∞-CATEGORIES

For an arbitrary symmetric monoidal∞-category V, we define the factorization homology of V-enriched∞-categories over (possibly stratified) 1-manifolds and study its basic properties. In the case that… Expand

The geometry of the cyclotomic trace

- David Ayala, Aaron Mazel-Gee, N. Rozenblyum
- Mathematics
- 17 October 2017

We provide a new construction of the topological cyclic homology $TC(C)$ of any spectrally-enriched $\infty$-category $C$, which affords a precise algebro-geometric interpretation of the cyclotomic… Expand

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