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]
[Erratum]

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. Toën, G. Vezzosi,
The l-adic trace formula for dg-categories and Bloch's conductor conjecture,
Research announcement, BUMI, 166 (2018), special issue in memory of Paolo De Bartolomeis, DOI: 10.1007/s40574-018-0166-0, Springer Verlag, p. 1-15 [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]

B. Toën, G. Vezzosi,
Trace formula for dg-categories and Bloch's conductor conjecture I,
Preprint arXiv:1710.05902 (first draft), October 2017, p. 1-41 [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. 1-8 [pdf]

M. Maggesi, G. Vezzosi,
Some elementary remarks on lci algebraic cycles,
[pdf] to appear in Rivista di Matematica della Università di Parma (2019)



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]

G. Vezzosi,
Derived critical loci I - Basics,
Note, September 2011, arXiv:1109.5213. [pdf]

M. Porta, G. Vezzosi,
Infinitesimal and square-zero extensions of simplicial algebras,
Note, pp. 1-32, October 2013, arXiv:1310.3573. [pdf]



Research Topics