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,
Caracteres de Chern, traces equivariantes et geometrie algebrique derivee,
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 Congres, 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, [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),, Springer Verlag, p. 3-17 [pdf]

B. Toën, G. Vezzosi,
Trace and K\"unneth formulas for singularity categories and applications,
Preprint (final submitted version), January 2019, p. 1-47 [pdf]

G. Vezzosi,
Appendix to: D. Anderson, R. Gonzales, S. Payne, Equivariant Grothendieck-Riemann-Roch and localization in operational K-theory,
Preprint arXiv:1907.00076 (submitted) , 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,
to appear in Panorama \&Synth\`ese, SMF (France), 2020, pp. 1-36. [pdf]

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]

Notes and Lecture Notes

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]

Research Topics