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Factorization homology I: higher categories
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, whichExpand
Crystals and D-modules
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
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 analogousExpand
A stratified homotopy hypothesis
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. AsExpand
Gaiotto’s Lagrangian Subvarieties via Derived Symplectic Geometry
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 symplecticExpand
DG Indschemes
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 concernExpand
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 thatExpand
The geometry of the cyclotomic trace
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 cyclotomicExpand