20 citations · 101 across the 24 of their papers we have counts for
28 papers
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…
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…
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.
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…
Grothendieck-Serre in the quasi-split unramified case
Kestutis Cesnavicius
The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group scheme over a regular local ring is trivial. We settle it in the c…
Purity for flat cohomology
Kestutis Cesnavicius, Peter Scholze
We establish the flat cohomology version of the Gabber-Thomason purity for étale cohomology: for a complete intersection Noetherian local ring and a commutative…
The Manin constant and the modular degree
Kestutis Cesnavicius, Michael Neururer, Abhishek Saha
The Manin constant of an elliptic curve over is the nonzero integer that scales the differential determined by the normalized newform associated to $…
Torsors on loop groups and the Hitchin fibration
Alexis Bouthier, Kestutis Cesnavicius
In his proof of the fundamental lemma, Ngô established the product formula for the Hitchin fibration over the anisotropic locus. One expects this formula over the larger genericall…
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…
Grothendieck-Lefschetz for vector bundles
Kestutis Cesnavicius
According to the Grothendieck-Lefschetz theorem from SGA 2, there are no nontrivial line bundles on the punctured spectrum of a local ring that is a complete intersection…
Purity for the Brauer group
Kestutis Cesnavicius
A purity conjecture due to Grothendieck and Auslander--Goldman predicts that the Brauer group of a regular scheme does not change after removing a closed subscheme of codimension $…
The -cohomology in the semistable case
Kestutis Cesnavicius, Teruhisa Koshikawa
For a proper, smooth scheme over a -adic field , we show that any proper, flat, semistable -model of whose logarithmic de Rham cohomology…
The Manin constant in the semistable case
Kestutis Cesnavicius
For an optimal modular parametrization of an elliptic curve over of conductor , Manin conjectured the agreement of two natural $\m…
Coarse base change fails for some modular curves
Kestutis Cesnavicius
For a congruence level , the formation of the modular curve , i.e., of the coarse moduli space of the level modular stack $\math…
The Manin-Stevens constant in the semistable case
Kestutis Cesnavicius
Stevens conjectured that for every optimal parametrization of an elliptic curve over of conductor , the pullback of some Néron di…
A modular description of
Kestutis Cesnavicius
As we explain, when a positive integer is not squarefree, even over the moduli stack that parametrizes generalized elliptic curves equipped with an ample cyclic su…
The remaining cases of the Kramer-Tunnell conjecture
Kestutis Cesnavicius, Naoki Imai
For an elliptic curve over a local field and a separable quadratic extension of , motivated by connections to the Birch and Swinnerton-Dyer conjecture, Kramer and Tunnel…
Poitou-Tate without restrictions on the order
Kestutis Cesnavicius
The Poitou-Tate sequence relates Galois cohomology with restricted ramification of a finite Galois module over a global field to that of the dual module under the assumption th…
-Selmer growth in extensions of degree
Kestutis Cesnavicius
There is a known analogy between growth questions for class groups and for Selmer groups. If is a prime, then the -torsion of the ideal class group grows unboundedly in $\ma…
Topology on cohomology of local fields
Kestutis Cesnavicius
Arithmetic duality theorems over a local field are delicate to prove if . In this case, the proofs often exploit topologies carried by the cohomology group…
The -parity conjecture over the constant quadratic extension
Kestutis Cesnavicius
For a prime and an abelian variety over a global field , the -parity conjecture predicts that, in accordance with the ideas of Birch and Swinnerton-Dyer, the $\…