43 citations · 154 across the 18 of their papers we have counts for
18 papers
Generically isotropic reductive group schemes are locally isotropic
Roman Fedorov
Let be a semilocal geometrically factorial Noetherian domain of characteristic zero. We show that a reductive -group scheme is isotropic if it is generically isotropic. We d…
Unramified Grothendieck-Serre for simply-connected group schemes satisfying an isotropy condition via unipotent chains
Roman Fedorov
We prove a case of the Grothendieck-Serre conjecture: let be a Noetherian semilocal flat algebra over a Dedekind domain such that all fibers of are geometrically regular; l…
Satake equivalence for Hodge modules on affine Grassmannians
Roman Fedorov
For a reductive group we equip the category of -equivariant polarizable pure Hodge modules on the affine Grassmannian with a structure of neutral…
On the purity conjecture of Nisnevich for torsors under reductive group schemes
Roman Fedorov
Let be a regular semilocal integral domain containing an infinite field . Let be an element such that for all maximal ideals of we have $f\notin\m…
Motivic Donaldson-Thomas Invariants of Parabolic Higgs Bundles and Parabolic Connections on a Curve
Roman Fedorov, Alexander Soibelman, Yan Soibelman
Let be a smooth projective curve over a field of characteristic zero and let be a non-empty set of rational points of . We calculate the motivic classes of moduli stacks…
On the Grothendieck-Serre Conjecture about principal bundles and its generalizations
Roman Fedorov
Let be a regular connected affine semi-local scheme over a field . Let be a reductive group scheme over . Assuming that has an appropriate parabolic subgroup sche…
Two circles and only a straightedge
Arseniy Akopyan, Roman Fedorov
We answer a question of David Hilbert: given two circles it is not possible in general to construct their centers using only a straightedge. On the other hand, we give infinitely m…
Motivic classes of moduli of Higgs bundles and moduli of bundles with connections
Roman Fedorov, Alexander Soibelman, Yan Soibelman
Let X be a smooth projective curve over a field of characteristic zero. We calculate the motivic class of the moduli stack of semistable Higgs bundles on X. We also calculate the m…
Variations of Hodge structures for hypergeometric differential operators and parabolic Higgs bundles
Roman Fedorov
Consider the holomorphic bundle with connection on corresponding to the regular hypergeometric differential operator \[ \prod_{j=1}^h(D-α_j)-z\prod_{j=…
On the Grothendieck-Serre conjecture on principal bundles in mixed characteristic
Roman Fedorov
Let R be a regular local ring. Let G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle over R is trivial if it is trivial ove…
Partial Fourier--Mukai transform for integrable systems with applications to Hitchin fibration
Dima Arinkin, Roman Fedorov
Let X be an abelian scheme over a scheme B. The Fourier--Mukai transform gives an equivalence between the derived category of X and the derived category of the dual abelian scheme.…
Affine Grassmannians of group schemes and exotic principal bundles over A^1
Roman Fedorov
Let G be a simple simply-connected group scheme over a regular local scheme U. Let E be a principal G-bundle over A^1_U trivial away from a subscheme finite over U. We show that E…
A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields
Roman Fedorov, Ivan Panin
Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over t…
An example of the Langlands correspondence for irregular rank two connections on P^1
Dmitry Arinkin, Roman Fedorov
Special kinds of rank 2 vector bundles with (possibly irregular) connections on P^1 are considered. We construct an equivalence between the derived category of quasi-coherent sheav…
Irregular Wakimoto modules and the Casimir connection
Roman M. Fedorov
We study some non-highest weight modules over an affine Kac-Moody algebra at non-critical level. Roughly speaking, these modules are non-commutative localizations of some non-highe…
Frobenius manifold structures on the spaces of abelian integrals
Roman M. Fedorov
Frobenius manifold structures on the spaces of abelian integrals were constructed by I. Krichever. We use D-modules, deformation theory, and homological algebra to give a coordinat…
Algebraic and hamiltonian approaches to isostokes deformations
Roman M. Fedorov
We study a generalization of the isomonodromic deformation to the case of connections with irregular singularities. We call this generalization Isostokes Deformation. A new deforma…
Upper bounds for the number of orbital topological types of planar polynomial vector fields "modulo limit cycles"
Roman M. Fedorov
The paper deals with planar polynomial vector fields. We aim to estimate the number of orbital topological equivalence classes for the fields of degree n. An evident obstacle for t…