78 citations · 260 across the 33 of their papers we have counts for
32 papers · 1 filter
Infinitesimal derived foliations
Bertrand Toën, Gabriele Vezzosi
We introduce a notion of \emph{infinitesimal derived foliation}. We prove it is related to the classical notion of infinitesimal cohomology, and satisfies some formal integrability…
Derived Foliations
Bertrand Toen, Gabriele Vezzosi
This is a book on derived foliations, that are a generalisation of classical foliations in the context of derived geometry. The text starts with the basic definitions and construct…
A flag version of Beilinson-Drinfeld Grassmannian for surfaces
Benjamin Hennion, Valerio Melani, Gabriele Vezzosi
In this paper we define and study a generalization of the Belinson-Drinfeld Grassmannian to the case where the curve is replaced by a smooth projective surface , and the trivial…
Foliations and stable maps
Bertrand Toën, Gabriele Vezzosi
This paper is part of an ongoing series of works on the study of foliations on algebraic varieties via derived algebraic geometry. We focus here on the specific case of globally de…
Algebraic foliations and derived geometry II: the Grothendieck-Riemann-Roch theorem
Bertrand Toën, Gabriele Vezzosi
This is the second of series of papers on the study of foliations in the setting of derived algebraic geometry based on the central notion of derived foliation. We introduce sheaf-…
Algebraic foliations and derived geometry: the Riemann-Hilbert correspondence
Bertrand Toën, Gabriele Vezzosi
This is the first in a series of papers about foliations in derived geometry. After introducing derived foliations on arbitrary derived stacks, we concentrate on quasi-smooth and r…
A remark on the Hochschild-Kostant-Rosenberg theorem in characteristic p
Benjamin Antieau, Gabriele Vezzosi
We prove a Hochschild-Kostant-Rosenberg decomposition theorem for smooth proper schemes in characteristic when . The best known previous result of this kind,…
Trace and Kunneth formulas for singularity categories and applications
Bertrand Toën, Gabriele Vezzosi
We present an -adic trace formula for saturated and admissible dg-categories over a base monoidal dg-category. Moreover, we prove Künneth formulas for dg-category of singular…
Some elementary remarks on lci algebraic cycles
Marco Maggesi, Gabriele Vezzosi
In this short note, we simply collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local…
Formal gluing along non-linear flags
Benjamin Hennion, Mauro Porta, Gabriele Vezzosi
In this paper we prove formal glueing along an arbitrary closed substack of an arbitrary Artin stack (locally of finite type over a field ), for the stacks of (almost) p…
Motivic Realizations of Singularity Categories and Vanishing Cycles
A. Blanc, M. Robalo, B. Töen +1
In this paper we establish a precise comparison between vanishing cycles and the singularity category of Landau-Ginzburg models over a complete discrete valuation ring. By using no…
The -adic trace formula for dg-categories and Bloch's conductor conjecture
B. Toën, G. Vezzosi
Building on recent results by A. Blanc, M. Robalo and the authors, we present an -adic trace formula for smooth and proper dg-categories over a base -alg…
Symplectic and Poisson derived geometry and deformation quantization
T. Pantev, G. Vezzosi
We review recent results and ongoing investigations of the symplectic and Poisson geometry of derived moduli spaces, and describe applications to deformation quantization of such s…
Shifted Poisson Structures and Deformation Quantization
D. Calaque, T. Pantev, B. Toen +2
This paper is the sequel to [PTVV] (IHES Vol. 117, 2013). We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and…
Infinitesimal and square-zero extensions of simplicial algebras
Mauro Porta, Gabriele Vezzosi
We introduce the notions of infinitesimal extension and square-zero extension in the context of simplicial commutatie algebras. We next investigate their mutual relationship and we…
Quadratic forms and Clifford algebras on derived stacks
Gabriele Vezzosi
In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over gen…
Derived Logarithmic Geometry I
Steffen Sagave, Timo Schürg, Gabriele Vezzosi
In order to develop the foundations of logarithmic derived geometry, we introduce a model category of logarithmic simplicial rings and a notion of derived log étale maps and use th…
Shifted Symplectic Structures
T. Pantev, B. Toen, M. Vaquie +1
This is the first of a series of papers about \emph{quantization} in the context of \emph{derived algebraic geometry}. In this first part, we introduce the notion of \emph{-shif…
Derived critical loci I - Basics
Gabriele Vezzosi
We will quickly explore the derived geometry of zero loci of sections of vector bundles, with particular emphasis on derived critical loci. In particular we will single out many of…
Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes
Timo Schürg, Bertrand Toën, Gabriele Vezzosi
We show how a quasi-smooth derived enhancement of a Deligne-Mumford stack X naturally endows X with a functorial perfect obstruction theory in the sense of Behrend-Fantechi. This r…
A note on the cotangent complex in derived algebraic geometry
Gabriele Vezzosi
This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation…
S^1-Equivariant simplicial algebras and de Rham theory
B. Toen, G. Vezzosi
This is a companion paper our previous submission "\infty-categories monoidales rigides et caracteres de Chern", in which we give a comparison between functions on the derived loop…
Homotopical Algebraic Geometry II: geometric stacks and applications
Bertrand Toen, Gabriele Vezzosi
This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and…
Segal topoi and stacks over Segal categories
Bertrand Toen, Gabriele Vezzosi
In math.AG/0207028 we began the study of higher sheaf theory (i.e. stacks theory) on higher categories endowed with a suitable notion of topology: precisely, we defined the notions…