Publications

Articles

  • (with A. Asok and M. Hopkins) Algebraic vector bundles and p-local A1-homotopy theory, Ann. Sci. ENS 58 (2025), no.5, 1155-1178.
  • (with N. Yang) On Tate Milnor-Witt motives, Ann. K-theory 10 (2025), no. 2, 153-187.
  • Suslin's cancellation conjecture in the smooth case, Duke Math. Journal 174 (2025), no.12, 2383-2423.
  • (with O. Haution) The stable Adams operations on Hermitian K-theory, Geom. Topol. 29 (2025), no.1, 127-169.
  • (with D. Coulette, F. Déglise and J. Hornbostel) Formal ternary laws and Buchstaber's 2-groups, Manuscripta Math. 174 (2023), 453-490.
  • (with A. Asok) Vector bundles on algebraic varieties, Proc. Int. Cong. Math. 2022, Vol. 3, 2146-2170, EMS Press, Berlin, 2023.
  • (with A. Asok and M. Hopkins) Localization and nilpotent spaces in A1-homotopy theory, Compos. Math. 158 (2022), no.3, 654-720.
  • (with F. Déglise) The Borel character, J. Inst. Math. Jussieu 22 (2023), no.2, 747-797.
  • (with F. Déglise, A. Khan and F. Jin) On the rational motivic homotopy category, J. Ec. Polytech., Math. 8 (2021), 533-583.
  • (with A. Asok) Euler class groups and motivic stable cohomotopy (with an appendix by M. K. Das), J. Eur. Math. Soc. 24 (2021), no.8, 2775-2822.
  • (with G. Berhuy and O. Garotta) Rank weights for arbitrary finite field extensions, Adv. Math. Commun. 15 (2021), no.4, 575-587.
  • (with A. Asok and B. Williams) Motivic spheres and the image of Suslin's Hurewicz map, Invent. Math. 219 (2020), no.1, 39-73.
  • Lectures on Chow-Witt groups, Motivic homotopy theory and refined enumerative geometry, Contemp. Math. (2019), 37 pages.
  • (with A. Asok and M. Hopkins) Obstructions to algebraizing topological vector bundles, Forum of Mathematics, Sigma 7 (2019), e6, 18 pages.
  • (with A. Dubouloz) Families of A1-contractible affine threefolds, Algebraic Geometry 5 (2018), no.1, 1-14.
  • (with A. Asok) Algebraic vs. topological vector bundles on spheres, J. Ramanujan Math. Soc. 32 (2017), 201-216.
  • (with A. Asok) An explicit KO-degree map and applications, J. Topology 10 (2017), 268-300.
  • The Vaserstein symbol on real smooth affine threefolds, K-Theory, TIFR Publications 19 (2018), 213-224.
  • (with A. Asok and B. Doran) Smooth models of motivic spheres and the clutching construction, IMRN 6 (2017), 1890-1925.
  • (with A. Asok) Comparing Euler classes, Q. J. Math. 67 (2016), 603-635.
  • On the number of generators of ideals in polynomial rings, Ann. of Math. 184 (2016), 315-331. Erratum: 186 (2017), 647-648.
  • (with A. Asok) Secondary characteristic classes and the Euler class, Documenta Math. (2015).
  • (with A. Asok) Splitting vector bundles outside the stable range and homotopy theory of punctured affine spaces, J. Amer. Math. Soc. 28 (2014), 1031-1062.
  • (with B. Calmès) Groupes classiques, Panoramas et Synthèses 46 (2015), 147 pages.
  • (with A. Asok) A cohomological classification of vector bundles over smooth affine threefolds, Duke Math. J. 163 (2014), 2561-2601.
  • (with A. Asok) Algebraic vector bundles on spheres, J. Topology 7 (2014), no. 3, 894-926.
  • (with S. M. Bhatwadekar and S. Sane) Euler class groups and 2-torsion element, J. Pure Appl. Algebra 218 (2014), 112-120.
  • The projective bundle theorem for Ij-cohomology, J. K-theory 11 (2013), no. 2, 413-464.
  • Mennicke symbols, K-cohomology and a Bass-Kubota theorem, Trans. Amer. Math. Soc. 367 (2015), no.1, 191-208.
  • (with R. Rao and R. Swan) On stably free modules over affine algebras, Publ. Math. IHES 116 (2012), 223-243.
  • A degree map on unimodular rows, J. Ramanujan Math. Soc. 27 (2012), no. 1, 21-40.
  • (with B. Calmès) Trivial Witt groups of flag varieties, J. Pure Appl. Algebra 216 (2012), 404?406.
  • Some remarks on orbit sets of unimodular rows, Comment. Math. Helv. 86 (2011), no.1, 13-39.
  • Stably free modules over smooth affine threefolds, Duke Math. Journal 156 (2011), no.1, 33-49.
  • Projective modules over the real 3-sphere, J. Algebra 325 (2011), no.1, 18-33.
  • The excess intersection formula for Grothendieck-Witt groups, Manuscripta Math. 130 (2009), no.4, 411-423.
  • (with V. Srinivas) Chow-Witt groups and Grothendieck-Witt groups of regular schemes, Adv. Math. 221 (2009), no.1, 302-329.
  • (with V. Srinivas) A vanishing theorem for oriented intersection multiplicities, Math. Res. Lett. 15 (2008), no.3, 447-458.
  • (with I. Dell'Ambrogio) The Witt groups of the spheres away from two, J. Pure Appl. Algebra 212 (2008), no.5, 1039-1045.
  • The Chow-Witt ring, Documenta Math. 12 (2007), 275-312.

Books

  • Groupes de Chow-Witt, Mém. Soc. Math. Fr. 113 (2008), 197 pages.
  • Milnor-Witt motives (with an [illustration] by Guillaume de Bats), Mem. Am. Math. Soc. 311 (2025), containing the following chapters:
  • (with B. Calmès) The category of finite Chow-Witt correspondences, 38 pages.
  • (with F. Déglise) MW-motivic complexes, 39 pages.
  • (with P. A. Ostvaer) A cancellation theorem for MW-correspondences, 18 pages.
  • (with B. Calmès) A comparison theorem for MW-motivic cohomology, 16 pages.
  • (with F. Déglise) The Milnor-Witt motivic ring spectrum and its associated theories, 37 pages.
  • (with T. Bachmann) On the effectivity of spectra representing motivic cohomology theories, 15 pages.

Preprints

  • (with F. Déglise) Quadratic Riemann-Roch formulas, 54 pages. [PDF]
  • (with A. Asok and S. Lerbet) Splitting vector bundles over real algebraic varieties, 39 pages.[PDF]

Other texts

  • The oriented Chow ring and applications, Oberwolfach Reports Vol. 3, issue 3, 1756-1757.
  • (with A. Asok) Toward a meta-stable range in A1-homotopy theory of punctured affine schemes, Oberwolfach Reports Vol. 10, issue 2, 1892-1895.
  • Le monde méconnu des modules projectifs, Gaz. Math., Soc. Math. Fr. 179 (2024), 25-31.