collaborators

6 papers

math.AG2025

Torsors on the complement of a smooth divisor

Kestutis Cesnavicius

We complete the proof of the Nisnevich conjecture in equal characteristic: for a smooth algebraic variety over a field , a -smooth divisor , and a reductive…

math.AG2025

Unramified Grothendieck-Serre for isotropic groups

Kestutis Cesnavicius, Roman Fedorov

The Grothendieck-Serre conjecture predicts that every generically trivial torsor under a reductive group over a regular semilocal ring is trivial. We establish this for unr…

math.AG2025

The affine Grassmannian as a presheaf quotient

Kestutis Cesnavicius

For a reductive group over a ring , its affine Grassmannian plays important roles in a wide range of subjects and is typically defined as the étale sheafifi…

math.AG2025

Problems about torsors over regular rings (with an appendix by Yifei Zhao)

Kestutis Cesnavicius

We overview a web of conjectures about torsors under reductive groups over regular rings and survey some techniques that have been used for making progress on such problems.

math.AG2025

Generically trivial torsors under constant groups

Alexis Bouthier, Kestutis Cesnavicius, Federico Scavia

We resolve the Grothendieck-Serre question over an arbitrary base field : for a smooth -group scheme and a smooth -variety , we show that every generically trivial…

math.AG2024

The analytic topology suffices for the -Grassmannian

Kestutis Cesnavicius, Alex Youcis

The -affine Grassmannian was introduced by Scholze in the context of the geometric local Langlands program in mixed characteristic and is the Fargues-Fontaine cu…