Papers
G. Vezzosi
Localization of differential operators and of higher order de Rham complexes
Rend. Sem. Mat. Univ. di Padova, Vol. 97 (1997), 113-133 [pdf]
G. Vezzosi, A.M. Vinogradov
Infinitesimal Stokes' formula for higher-order de Rham complexes
Acta Appl. Math., Vol. 49, N. 3 (1997), 311-329 [pdf]
G. Vezzosi
On the Chow ring of the classifying stack of PGL(3)
Journal für die reine und angewandte Mathematik (Crelle), 523 (2000), 1-54 [pdf]
G. Vezzosi
Brown-Peterson spectra in stable 𝔸^1-homotopy theory,
Rend. Sem. Mat. Univ. di Padova, Vol. 106 (2001), 47-64 [pdf]
G. Vezzosi, A. Vistoli
Higher algebraic K-theory of group actions with finite stabilizers
Duke Math. J., 113 (2002), 1-55 [pdf]
G. Vezzosi, A. M. Vinogradov
On higher order analogues of de Rham cohomology
Diff. Geom. Appl., 19 (2003) 29-59 [pdf]
G. Vezzosi, A. Vistoli
Higher algebraic K-theory for actions of diagonalizable groups
Inventiones Math., 153, Number 1 (2003), 1-44. [pdf]
S. Schröer, G. Vezzosi
Existence of vector bundles and global resolutions for singular surfaces
Compositio Math., 140/3 (2004), 717-728 [pdf]
B. Toën, G. Vezzosi,
From HAG to DAG: Derived moduli spaces
p. 175-218, in Axiomatic, Enriched and Motivic Homotopy Theory, Proceedings of the NATO Advanced Study Institute, Cambridge, UK, (9-20 September 2002), Ed. J.P.C. Greenlees, NATO Science Series II, Volume 131 Kluwer, 2004 [pdf]
B. Toën, G. Vezzosi
A remark on K-theory and S-categories
Topology, 43 (2004), 765-791 [pdf]
B. Toën, G. Vezzosi
Homotopical Algebraic Geometry I: Topos theory
Advances in Math., Volume 193, Issue 2 , 1 June 2005, p. 257-372. [pdf]
B. Toën, G. Vezzosi
"Brave New" algebraic geometry and global derived moduli spaces of ring spectra
in Elliptic cohomology: geometry, applications & higher chromatic analogues London Mathematical Society lecture notes series, 342
p. 325-359, H. Miller, D. Ravenel eds., 2007 [pdf]
B. Toën, G. Vezzosi
Homotopical Algebraic Geometry II: Geometric stacks and applications
pp. 1-228, Memoirs of the American Mathematical Society, May 2008, volume 193, number 902 [pdf]
B. Toën, G. Vezzosi
A note on Chern characters, loop spaces and derived algebraic geometry
pp. 331-354, in 2007 Abel Prize Proceedings [pdf]
B. Toën, G. Vezzosi
Algebres simpliciales S^1-equivariantes, theorie de de Rham et theoremes HKR multiplicatifs
Compositio Math. 147/06 (2011), Pages 1979-2000. [pdf]
G. Vezzosi
What is ... a derived stack?
p. 955-958, Notices AMS, August 2011, Volume 58, Issue 07 [pdf]
T. Schürg, B. Toën, G. Vezzosi
Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes
p. 1-42, Journal für die reine und angewandte Mathematik (Crelle), DOI: 10.1515/crelle-2013-0037, June 2013 [pdf]
T. Pantev, B. Toën, M. Vaquie, G. Vezzosi
Shifted Symplectic Structures
Publ. Math. IHES, June 2013, Volume 117, Issue 1, pp 271-328 [pdf]
B. Toën, G. Vezzosi
Caractères de Chern, traces équivariantes et géométrie algébrique derivée
Selecta Math. Volume 21, Issue 2, pp 449-554 (2015) [pdf]
S. Sagave, T. Schürg, G. Vezzosi
Logarithmic Derived Geometry I
Journal of the Institute of Mathematics of Jussieu, 15 (2016), no. 2, 367-405 [pdf]
G. Vezzosi
A model structure on relative dg-Lie algebroids
in Stacks and Categories in Geometry, Topology, and Algebra, Contemporary Mathematics (AMS), 643 (2015) [pdf]
G. Vezzosi
Quadratic forms and Clifford algebras on derived stacks
Advances in Mathematics Volume 301, 1 October 2016, Pages 161-203 [pdf]
D. Calaque, T. Pantev, B. Toën, M. Vaquie, G. Vezzosi
Shifted Poisson Structures and Deformation Quantization
Journal of Topology, Vol: 10, Pages: 483-584 (June 2017) DOI: 10.1112/topo.12012 [pdf]
B. Hennion, M. Porta, G. Vezzosi
Formal glueing for nonlinear flags
Preprint arXiv:1607.04503v2, October 2016, p. 1-78 [pdf]
B. Toën, G. Vezzosi
Géométrie non-commutative, formule des traces et conducteur de Bloch
Seminaires et Congrés, 31, Soc. Math. de France (2018), Actes du 1er congres national de la SMF - C. Lecouvrey, ed., p. 77-107 (2018), p. 1-23 [pdf]
T. Pantev, G. Vezzosi
Symplectic and Poisson derived geometry and deformation quantization
Algebraic Geometry - Proceedings of the AMS Summer Institute, University of Utah, Salt Lake City, Proceedings of Symposia in Pure Mathematics, Volume 97/2, 2018, p. 405-457, http://dx.doi.org/10.1090/pspum/097.2/01712 [pdf]
A. Blanc, M. Robalo, B. Toën, G. Vezzosi
Motivic Realizations of Singularity Categories and Vanishing Cycles
Journal de l'Ecole Polytechnique, 5 (2018), p. 651-747, doi : 10.5802/jep.81 [pdf]
B. Antieau, G. Vezzosi
A remark on the Hochschild-Kostant-Rosenberg theorem in characteristic p
to appear in Annali della Scuola Normale Superiore, October 2018, p. 1-9, DOI Number: 10.2422/2036-2145.201711_007 [pdf]
M. Maggesi, G. Vezzosi
Some elementary remarks on lci algebraic cycles
Riv. Mat. Univ. Parma Vol. 9 (2018), 365-372 [pdf]
B. Toën, G. Vezzosi
The ℓ-adic trace formula for dg-categories and Bloch's conductor conjecture
BUMI, volume 12 (2019), https://doi.org/10.1007/s40574-018-0166-0, Springer Verlag, p. 3-17 [pdf]
G. Vezzosi
Appendix to: D. Anderson, R. Gonzales, S. Payne, Equivariant Grothendieck-Riemann-Roch and localization in operational K-theory
Algebra and Number Theory 15 (2021), no. 2, 341–385 (Revised version March 2020, p. 36-43) [pdf]
B. Toën, G. Vezzosi
Algebraic foliations and derived geometry I: the Riemann-Hilbert correspondence
Preprint arXiv:2001.05450, January 2020, p. 1-46 [link]
G. Vezzosi
Basic structures on derived critical loci
Differential Geometry and Applications, Volume 71, August 2020 -
Special issue on Geometry of PDE's -
In memory of Alexandre Mikhailovich Vinogradov, p. 1-12 [pdf]
T. Pantev, G. Vezzosi
Introductory topics in derived algebraic geometry
Panorama & Synthèse, SMF (France), 2020, pp. 1-36. [pdf]
B. Toën, G. Vezzosi
Trace and Künneth formulas for singularity categories and applications
Compositio Mathematica , Volume 158 , Issue 3 , March 2022 , pp. 483 - 528 [pdf]
B. Toën, G. Vezzosi
Algebraic foliations and derived geometry : the Riemann-Hilbert correspondence
Selecta Math. (2023) 29:5, p. 1-47 https://doi.org/10.1007/s00029-022-00808-9
B. Toën, G. Vezzosi
Algebraic foliations and derived geometry II: the Grothendieck-Riemann-Roch theorem
Preprint arXiv 2007.09251, July 2020, p. 1-40 [link]
B. Toën, G. Vezzosi
Foliations and stable maps
Preprint arXiv:2202.09174, to appear in Simons Symposia, Proceedings of the IMSA conference on "Current Developments in Hodge Theory" (Springer Nature), 2025, p. 1-33 [link]
B. Toën, G. Vezzosi
Infinitesimal derived foliations
Preprint arXiv:2305.13010, May 2023, p. 1-19 [link]
B. Hennion, V. Melani, G. Vezzosi
A flag version of Beilinson-Drinfeld Grassmannian for surfaces
Preprint arXiv:2210.04798, final version to appear in Moduli (Foundation Compositio Mathematica) p. 1-74 [pdf]
V. Melani, H. Pourcelot, G. Vezzosi
Tate modules as condensed modules
Preprint arXiv:2501.07481v2, January 2025, p. 1-15 [link] (submitted)
A. Maffei, V. Melani, G. Vezzosi
Two dimensional versions of the affine Grassmannian and their geometric description
Preprint arXiv:2503.16353, March 2025, p. 1-40 [link] (to appear in Forum of Mathematics, Sigma)
B. Toën, G. Vezzosi
Derived Foliations
Research Monograph (first draft), August 2025 p. 1-258 [link] (submitted)
G. Vezzosi
The Chow ring of PGL(2) is generated by Chern classes of the adjoint representation
Note, SNS, Pisa, June 1998 [pdf]
B. Toën, G. Vezzosi
From homotopical algebra to homotopical algebraic geometry
Lectures at the DFG-Schwerpunkt Workshop, Essen, October, 25-26 2002 (organized by H. Esnault, S. Müller-Stach, E. Viehweg). [pdf]
B. Toën, G. Vezzosi
Segal topoi and stacks over Segal sites
p. 1-22, Preprint (arXiv:math/0212330), last 2008 version [pdf]
G. Vezzosi
A sketchy note on enriched homotopical topologies and enriched homotopical stacks
Note, math.CT/0507447. [pdf]
G. Vezzosi
A note on the cotangent complex in derived algebraic geometry
Note, July 2010, arXiv:1008.0601. [pdf]
M. Porta, G. Vezzosi
Infinitesimal and square-zero extensions of simplicial algebras
Note, pp. 1-32, October 2013, arXiv:1310.3573. [pdf]
G. Vezzosi
Symmetric algebra of a cochain complex: cheat-sheet
Note, pp. 1-14, July 2019, Notes for students. [pdf]