3 citations · 3 across the 3 of their papers we have counts for
7 papers · 1 filter
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…
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 sheafific…
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…
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…
Reconstructing a variety from its topology (after Kollár, building on earlier work of Lieblich and Olsson)
Kestutis Cesnavicius
We survey a recent result of Kollár about reconstructing normal, geometrically integral, projective varieties of dimension in characteristic from their underlying Zaris…
Macaulayfication of Noetherian schemes
Kestutis Cesnavicius
To reduce to resolving Cohen-Macaulay singularities, Faltings initiated the program of "Macaulayfying" a given Noetherian scheme . For a wide class of , Kawasaki built the so…