Kęstutis Česnavičius

Institut de Mathématiques de Jussieu - Paris Rive Gauche
Sorbonne Université
4 place Jussieu, Bureau 15-25 411
F-75005 Paris, France

Office:   15-25 411
E-mail:  kestutis@imj-prg.fr

I am a directeur de recherche of the CNRS located at Sorbonne Université.
See my CV for details.

Research articles

• Generically trivial torsors under constant groups (joint with Alexis Bouthier and Federico Scavia), submitted.
  For a smooth group G over a field k, we show that generically trivial G-torsors over smooth varieties are Zariski locally trivial.


• The analytic topology suffices for the B⁺_dR-Grassmannian(joint with Alex Youcis), accepted to the Proceedings of the Simons Symposium on p-adic Hodge theory (2022).
  


• Unramified Grothendieck–Serre for isotropic groups (joint with Roman Fedorov), accepted to JEMS, doi:10.4171....
  


• The affine Grassmannian as a presheaf quotient, Comptes Rendus Mathématique, Académie des Sciences, Paris, 363 (2025), 523–532, doi:10.58....
  


• Torsors on the complement of a smooth divisor, Cambridge Journal of Mathematics, 12 (2024), no. 4, 903–936, doi:10.4310/....
  


• The Manin constant and the modular degree (joint with Michael Neururer and Abhishek Saha), JEMS, 26 (2024), no. 2, 573–637, doi:10.4....
  


• Purity for flat cohomology (joint with Peter Scholze), Annals of Mathematics, 199 (2024), no. 1, 51–180, doi:10.4007/....
  


• 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_inf-cohomology in the semistable case (joint with Teruhisa Koshikawa), 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 X₀(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/....

Expository writing

• 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.