Papers

G. Vezzosi, A.M. Vinogradov,
Infinitesimal Stokes' formula for higher-order de Rham complexes,
Acta Appl. Math., Vol. 49, N. 3 (1997), 311-329.

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.

G. Vezzosi,
Brown-Peterson spectra in stable A^1-homotopy theory,
Rend. Sem. Mat. Univ. di Padova, Vol. 106 (2001), 47-64.

G. Vezzosi, A. Vistoli,
Higher algebraic K-theory of group actions with finite stabilizers,
Duke Math. J., 113 (2002), 1-55.

G. Vezzosi, A. M. Vinogradov,
On higher order analogues of de Rham cohomology,
Diff. Geom. Appl., 19 (2003) 29-59.

G. Vezzosi, A. Vistoli,
Higher algebraic K-theory for actions of diagonalizable groups,
Inventiones Math., 153, Number 1 (2003), 1-44.

S. Schröer, G. Vezzosi,
Existence of vector bundles and global resolutions for singular surfaces,
Compositio Math., 140/3 (2004), 717-728.

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.

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,
p. 1-18, to appear in a slightly revised form in 2007 Abel Prize Proceedings [pdf]

B. Toën, G. Vezzosi,
Caracteres de Chern, traces equivariantes et geometrie algebrique derivee,
p. 1-84, submitted version Febr. 2011 [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. Schurg, B. Toën, G. Vezzosi,
Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes,
p. 1-42, April 2013, to appear in Journal für die reine und angewandte Mathematik (Crelle) [pdf]

T. Pantev, B. Toën, M. Vaquie, G. Vezzosi,
Shifted Symplectic Structures,
p. 1-52, April 2013, to appear in Publ. Math. IHES [pdf]

Notes and Lecture Notes

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]

G. Vezzosi,
A model structure on relative dg-Lie algebroids,
Note, April 2013, arXiv:1304.6049. [pdf]

Research Topics