Publications


(with G. Berhuy and O. Garotta) Rank weights for arbitrary finite field extensions, 12 pages, accepted for publication in Adv. Math. Commun.

(with A. Asok and B. Williams) Motivic spheres and the image of the Suslin-Hurewicz map, Invent. Math. 219 (2020), no.1, 39-73.

Lectures on Chow-Witt groups, "Motivic homotopy theory and refined enumerative geometry", Contemp. Math. 745 (2020), 83-121.

(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, Alg. Geom. 5 (2018), no.1, 1-14.

(with A. Asok) Algebraic vs. topological vector bundles on spheres, J. Ramanujan Math. Soc. 32 (2017), no. 3, 201-216.

(with A. Asok) An explicit KO-degree map and applications, J. Topology 10 (2017), no. 1, 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), no.1, 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. (2) 184 (2016), no.1, 315-331. Erratum: Ann. of Math. (2) 186 (2017), 647-648.

(with A. Asok) Secondary characteristic classes and the Euler class, Documenta Math. Extra volume: Alexander S. Merkurjev Sixtieth Birthday (2015).

(with A. Asok) Splitting vector bundles outside the stable range and homotopy theory of punctured affine spaces, J. Amer. Math. Soc. 28 (2014), no.4, 1031-1062.

(with B. Calmès) Groupes classiques, 147 pages, Panoramas et Synthèses 46 (2015).

(with A. Asok) A cohomological classification of vector bundles over smooth affine threefolds, Duke Math. Journal 163 (2014), no.14, 2561-2601.

(with A. Asok) Algebraic vector bundles on spheres, J. Topology 7 (2014), no. 3, 894-926.

(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), no. 2, 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.

Groupes de Chow-Witt, Mém. Soc. Math. Fr. 113 (2008), 197 pages.

(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.


Preprints


(with B. Calmès) The category of finite Chow-Witt correspondences, 47 pages. [PDF]

(with A. Asok) Euler class groups and motivic stable cohomotopy, 30 pages. [PDF]

(with F. Déglise) MW-motivic complexes, 30 pages. [PDF]

(with P. A. Ostvaer) A cancellation theorem for MW-correspondences, 21 pages. [PDF]

(with B. Calmès) A comparison theorem for MW-motivic cohomology, 17 pages. [PDF]

(with F. Déglise) The Milnor-Witt motivic ring spectrum and its associated theories, 37 pages. [PDF]

(with T. Bachmann) On the effectivity of spectra representing motivic cohomology theories, 12 pages. [PDF]

(with A. Asok and M. Hopkins) Localization and nilpotent spaces in A1-homotopy theory, 62 pages. [PDF]

(with A. Asok and M. Hopkins) Algebraic vector bundles and p-local A1-homotopy theory, 18 pages. [PDF]

(with F. Déglise, A. Khan and F. Jin) On the rational motivic homotopy category, 52 pages. [PDF]

(with F. Déglise) The Borel character, 49 pages. [PDF]

(with O. Haution) The stable Adams operations on Hermitian K-theory, 24 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.