Institut de Mathématique d'Orsay

Université Paris-Sud

Bâtiment 307, Bureau 3E22

F-91405 Orsay Cedex

**Office: ** 3E22

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

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

See my
CV for details.

- Grothendieck-Lefschetz for vector bundles,
*submitted.*

We extend the Grothendieck-Lefschetz theorem from SGA 2 about the triviality of line bundles on the punctured spectra of complete intersections to vector bundles. - Purity for the Brauer group,
*submitted.*

We complete the proof of a purity conjecture of Grothendieck: the cohomological Brauer group is insensitive to removing a closed subscheme of codimension ≥ 2 of a regular scheme. - The A
_{inf}-cohomology in the semistable case (joint with Teruhisa Koshikawa),*submitted.*

We extend the A_{inf}-cohomology of Bhatt–Morrow–Scholze to the case of semistable reduction and use it to analyze lattices in de Rham cohomology and reprove the Fontaine–Jannsen conjecture. - The Manin–Stevens constant in the semistable case,
*submitted.*

We prove the semistable case of a conjecture of Stevens about optimal modular parametrizations of elliptic curves by X_{1}(n). - The Manin constant in the semistable case,
*accepted to Compositio Mathematica.*

- The ℓ-parity conjecture over the constant quadratic extension,
*accepted to Mathematical Proceedings of the Cambridge Philosophical Society*, doi:10.1017/S030500411700055X. - A modular description of X
_{0}(n),*Algebra and Number Theory*,**11**(2017), no. 9, 2001-2089, doi:10.2140/ant.2017.11.2001.

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/AG-2017-023. - p-Selmer growth in extensions of degree p,
*Journal of the London Mathematical Society*,**95**(2017), no. 3, 833-852, doi:10.1112/jlms.12038. - The remaining cases of the Kramer–Tunnell conjecture (joint with Naoki Imai),
*Compositio Mathematica,***152**(2016), 2255-2268, doi:10.1112/S0010437X16007624. - 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/crelle-2014-0040.

- Selmer groups as flat cohomology groups,
*Journal of the Ramanujan Mathematical Society,***31**(2016), no. 1, 31-61.

My PhD thesis 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/S1793042116500159. - Poitou–Tate without restrictions on the order,
*Mathematical Research Letters,***22**(2015), no. 6, 1621-1666, doi:10.4310/MRL.2015.v22.n6.a5. - Topology on cohomology of local fields,
*Forum of Mathematics, Sigma*,**3**(2015), e16, 55 pp., doi:10.1017/fms.2015.18. - Selmer groups and class groups,
*Compositio Mathematica*,**151**(2015), no. 3, 416-434, doi:10.1112/S0010437X14007441.

- Identification of the graded pieces,
*Oberwolfach extended abstract.*

The write up of a 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.