Publications

  • Théorèmes de Riemann-Roch pour les champs de Deligne-Mumford. K-theory 18 (1999), No. 1 33-76. PDF
  • On motives for Deligne-Mumford stacks. IMRN No. 17 (2000), 909-928. PDF
  • Vers une interprétation Galoisienne de la théorie de l’homotopie. Cahiers de Top. et de Geo. Diff. Cat. 43, No. 4 (2002), 257-312. PDF
  • (joint with Vezzosi) Homotopical Algebraic Geometry I: Topos theory. Adv. in Math. 193 (2005), 257-372. PDF
  • (joint with Vezzosi) A remark on K-theory and S-categories. Topology 43, No. 4 (2004), 765-791. PDF
  • (joint with Vezzosi) From HAG to DAG: derived moduli spaces. in Axiomatic, enriched and motivic homotopy theory, 173-216, NATO Sci. Ser. II Math. Phys. Chem., 131, Kluwer Acad. Publ., Dordrecht, 2004. PDF
  • (joint with Kock) Simplicial localization of monoidal structures, and a non-linear version of Deligne’s conjecture. Compos. Math. 141 (2005), no. 1, 253-261. PDF
  • (joint with Vezzosi) Brave new algebraic geometry. in Elliptic cohomology, 325–359, London Math. Soc. Lecture Note Ser., 342, Cambridge Univ. Press, Cambridge, 2007. PDF
  • Vers une axiomatisation de la théorie des catégories supérieures. K-Theory 34 (2005), no. 3, 233-263. PDF
  • (joint with Vezzosi) Homotopical Algebraic Geometry II: geometric stacks and applications. Mem. Amer. Math. Soc. 193 (2008), no. 902, x+224 pp. PDF
  • Champs affines. Selecta Math. (N.S.) 12 (2006), no. 1, 39-135. PDF
  • Derived Hall algebra. Duke Math. J. 135 (2006), no. 3, 587-615. PDF
  • The homotopy theory of dg-categories and derived Morita theory. Invent. Math. 167 (2007), no. 3, 615-667. PDF
  • (joint with Vaquié) Moduli of objects in dg-categories. Ann. Sci. de l’ENS Volume 40 (2007) Issue 3, Pages 387-444. PDF
  • (joint with M. Anel) Dénombrabilité des classes d’équivalences dérivées de variétés algébriques. J. Algebraic Geom. 18 (2009), no. 2, 257-277. PDF
  • (joint with Vaquié) Au-dessous de Spec Z. J. K-Theory 3 (2009), no. 3, 437–500. PDF
  • Anneaux de définition des dg-algèbres propres et lisses Bull. Lond. Math. Soc. 40 (2008), no. 4, 642-650. PDF
  • Finitude homotopique des dg-algèbres propres et lisses. Proc. Lond. Math. Soc. (3) 98 (2009), no. 1, 217-240. PDF
  • (joint with Katzarkov and Pantev) Schematic homotopy types and non-abelian Hodge theory. Compos. Math. 144 (2008), no. 3, 582-632. PDF
  • (joint with Vaquié) Algébrisation des variétés analytiques complexes et catégories dérivées Math. Ann. (2008) 342, 789-831. PDF
  • (joint with Katzarkov and Pantev) Algebraic and topological aspects of the schematization functor. Compos. Math. 145 (2009), no. 3, 633-686. PDF
  • Higher and derived stacks: a global overview. Algebraic geometry—Seattle 2005. Part 1, 435–487, Proc. Sympos. Pure Math., 80, Part 1, Amer. Math. Soc., Providence, RI, 2009. PDF
  • (joint with Vezzosi) A note on Chern character, loop spaces and derived algebraic geometry. Abel Symposium, Oslo 2007. PDF
  • Lectures on dg-categories, for the Sedano winter school on K-theory, LNM 2008. PDF
  • Descente fidèlement plate pour les n-champs d’Artin.  Compos. Math. 147 (2011), no. 5, 1382-1412. PDF
  • Derived algebraic geometry, in, Simplicial methods for operads and algebraic geometry. Advanced course in Mathematics – CRM Barcelona series. PDF
  • (joint with Vezzosi) Algèbres simpliciales S^1-équivariantes et théorie de de Rham. Compos. Math. 147 (2011), no. 6, 1979-2000. PDF
  • Derived Azumaya algebras and genertors for twisted derived categories. Invent. Math. 189 (2012), no. 3, 581–652. PDF
  • (joint with Pantev, Vaquié and Vezzosi) Shifted symplectic structures. Publ. Math. Inst. Hautes Études Sci. 117 (2013), 271-328.  PDF
  • (joint with Schurg and Vezzosi) Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes. J. Reine Angew. Math. 702, 1 – 40 (2015).  PDF
  • (joint with Vezzosi) Infinie-catégories monoidales rigides et caractères de Chern. Sel. Math., New Ser. 21, No. 2, 449 – 554 (2015). PDF
  • Derived Algebraic Geometry. EMS Surv. Math. Sci. 1 (2014), no. 2, 153-245.PDF
  • Derived Algebraic Geometry and Deformation Quantization. ICM lecture. PDF
  • Problèmes de modules formels. Exposé Bourbaki du 16 Janvier 2016. PDF
  • (avec Vaquié) Systèmes de points dans les dg-catégories saturées. Ann. Fac. Sci. Toulouse, Math. (6) 25, No. 2-3, Part B, 583 – 618 (2016). PDF
  • (with Calaque, Pantev, Vaquié and Vezzosi) Shifted Poisson structures.  J. of Topology, Volume 10, Issue 2 June 2017 Pages 483 – 584. PDF
  • (with Vezzosi) Géométrie non-commutative, formule des traces et conducteur de Bloch. Actes du 1er Congrès de la SMF—Tours, 2016, 77–107, Sémin. Congr., 31, SMF, Paris, 2017. PDF
  • (with Vezzosi) The l-adic trace formula for dg-categories and Bloch’s conductor conjecture,  Boll. Unione Mat. Ital. 12 (2019), no. 1-2, 3–17. PDF
  • (with Blanc, Robalo and Vezzosi) Matrix factorizations and vanishing cycles, J. Ec. polytech. Math. 5 (2018), 651–747. PDF
  • (with Pantev) Poisson geometry  of the  moduli of   local systems on smooth varieties. Publ. Res. Inst. Math. Sci. 57 (2021), no. 3-4, 959–991. PDF
  • Le problème de la schématisation revisité. EPIGA, volume 4 (2020), Article no. 14. PDF
  • (with Moulinos and Robalo) A universal HKR theorem. Geom. Topol. 26 (2022), no. 2, 777–874. PDF
  • (with Vezzosi) Trace and Kunneth formulas for singularity categories and applications. Compos. Math. 158 (2022), no. 3, 483–528. PDF
  • (with Pantev) Moduli of flat connections on smooth varieties. Algebr. Geom. 9 (2022), no. 3, 266–310. PDF
  • (with Vezzosi) Algebraic foliations and derived geometry: the Riemann-Hilbert correspondence. Selecta Math. (N.S.) 29 (2023), no. 1, Paper No. 5, 47 pp. PDF
  • (with Vezzosi) Foliations and stable maps in Current developments in Hodge theory. Simons Symp. Springer, Cham, 2025 PDF
  • Generalized local jacobians and commutative group stacks. To appear in Annales de la Factulté de Sciences de Toulouse. PDF