Institut de Mathématique d'Orsay
Université Paris-Saclay Bâtiment 307, Bureau 3E22 F-91405 Orsay, France
Office phone: 01 69 15 57 44
I am a chargé de recherche of CNRS located at the Université Paris-Saclay.
CV for details.
Postdoc positions are available starting in the Fall 2024, see
for details. Deadline: January 10, 2024.
Unramified Grothendieck–Serre for isotropic groups (joint with Roman Fedorov), submitted.
We show that a generically trivial torsor under a totally isotropic reductive group over an unramified semilocal regular ring is trivial.
The analytic topology suffices for the B + dR -Grassmannian (joint with Alex Youcis), submitted.
We show that Scholze's B + dR -affine Grassmannian is the analytic sheafification of the presheaf quotient LG/L
Torsors on the complement of a smooth divisor, submitted.
We complete the proof of the equal characteristic case of the Nisnevich conjecture about generically trivial torsors defined on the complement of a smooth divisor and show that sheafification is often not needed for defining the affine Grassmannian.
Purity for flat cohomology (joint with Peter Scholze), Annals of Mathematics, to appear.
The Manin constant and the modular degree (joint with Michael Neururer and Abhishek Saha), J. Eur. Math. Soc., to appear.
Torsors on loop groups and the Hitchin fibration (joint with Alexis Bouthier), Annales scientifiques de l'ENS, 55 (2022), no. 3, 791–864, doi:10....
Problems about torsors over regular rings (with an appendix by Yifei Zhao), Acta Mathematica Vietnamica, 47 (2022), no. 1, 39–107, doi:10.1....
Grothendieck–Serre in the quasi-split unramified case, Forum of Mathematics, Pi, 10 (2022), e9, 30 pp., doi:10.1017/....
Macaulayfication of Noetherian schemes, Duke Mathematical Journal, 170 (2021), no. 7, 1419–1455, doi:10.1215/....
Grothendieck–Lefschetz for vector bundles,
Algebraic Geometry, 7 (2020), no. 4, 503–511, doi:10.14231/....
The A (joint with Teruhisa Koshikawa), inf-cohomology in the semistable case
Compositio Mathematica, 155 (2019), no. 11, 2039–2128, doi:10....
Purity for the Brauer group, Duke Mathematical Journal, 168 (2019), no. 8, 1461–1486, doi:10.1215/....
The Manin constant in the semistable case, Compositio Mathematica, 154 (2018), no. 9, 1889–1920, doi:10.1112/....
The related earlier preprint The Manin–Stevens constant in the semistable case presents a different approach.
The ℓ-parity conjecture over the constant quadratic extension,
Math. Proc. Cambridge Phil. Soc., 165 (2018), no. 3, 385–409, doi:10.1017/....
A modular description of X, 0(n) Algebra and Number Theory, 11 (2017), no. 9, 2001–2089, doi:10.2140/....
Here is the letter of Deligne referenced in the article.
Coarse base change fails for some modular curves,
Algebraic Geometry, 4 (2017), no. 4, 444–451, doi:10.14231/....
p-Selmer growth in extensions of degree p,
Journal of the London Mathematical Society, 95 (2017), no. 3, 833–852, doi:10.1112/....
The remaining cases of the Kramer–Tunnell conjecture (joint with Naoki Imai),
Compositio Mathematica, 152 (2016), 2255–2268, doi:10.1112/....
The p-parity conjecture for elliptic curves with a p-isogeny, Journal für die reine und angewandte Mathematik, 719 (2016), 45–73, doi:10.1515/....
Selmer groups as flat cohomology groups, Journal of the Ramanujan Mathematical Society, 31 (2016), no. 1, 31–61, jrms:2016-031-001/....
My PhD thesis (official version here) also discusses several tangentially related questions.
Local factors valued in normal domains,
International Journal of Number Theory, 12 (2016), no. 1, 249–272, doi:10.1142/....
Poitou–Tate without restrictions on the order,
Mathematical Research Letters, 22 (2015), no. 6, 1621–1666, doi:10.4310/....
Topology on cohomology of local fields,
Forum of Mathematics, Sigma, 3 (2015), e16, 55 pp., doi:10.1017/....
Selmer groups and class groups,
Compositio Mathematica, 151 (2015), no. 3, 416–434, doi:10.1112/....
Reconstructing a variety from its topology,
Astérisque, 430, Séminaire Bourbaki. Vol. 2019/2021. Exposé 1175 (2021), 275–293, doi:10.24033/.... The write up of my talk at Séminaire Bourbaki, April 2021.
Invariance under Henselian pairs for flat cohomology,
Oberwolfach extended abstract, doi:10.4171/.... The write up of my talk at the Oberwolfach workshop "Arithmetic Geometry," July 2020.
Identification of the graded pieces,
Oberwolfach extended abstract, doi:10.4171/.... The write up of my talk at the Arbeitsgemeinschaft "Topological cyclic homology," April 2018.
Integral relations between p-adic cohomology theories
A plan for the UC Berkeley number theory learning seminar, Spring 2017.
Rational points and obstructions to their existence and the abridged version that excludes hints and side remarks.
A problem set for the Arizona Winter School 2015.
Obstructions to rational points via étale homotopy Notes from the talk I gave at the MIT graduate student algebraic geometry and number theory seminar STAGE in December 2011.
l-adic perverse sheaves An expository term paper written for the Harvard class Perverse Sheaves in Representation Theory in Fall 2011.