Institut de Mathématique d'Orsay

Université Paris-Saclay

Bâtiment 307, Bureau 3E22

F-91405 Orsay, France

**Office: ** 3E22

**Office phone: ** 01 69 15 57 44

**E-mail:** kestutis@math.u-psud.fr

I am a chargé de recherche of CNRS located at the Université Paris-Saclay.

See my
CV for details.

Postdoc positions are available starting in the Fall 2024, see this pdf 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^{+}G. - 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
_{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 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.