21 citations · 61 across the 14 of their papers we have counts for
16 papers
Morava K-theory and Rost invariant
Andrei Lavrenov, Victor Petrov
We prove that inner forms of a variety of Borel subgroups have isomorphic motives with respect to the second Morava K-theory if and only if the corresponding Tits algebras and Rost…
The Allison-Faulkner construction of
Victor Petrov, Simon W. Rigby
We show that the Tits index cannot be obtained by means of the Tits construction over a field with no odd degree extensions. We construct two cohomological invariants,…
Morava K-theory of orthogonal groups and motives of projective quadrics
Nikita Geldhauser, Andrei Lavrenov, Victor Petrov +1
We compute the algebraic Morava K-theory ring of split special orthogonal and spin groups. In particular, we establish certain stabilization results for the Morava K-theory of spec…
Hopf-theoretic approach to motives of twisted flag varieties
Victor Petrov, Nikita Semenov
Let be a split semisimple algebraic group over a field and let be an oriented cohomology theory in the sense of Levine--Morel. We provide a uniform approach to the -…
Rost motives, affine varieties, and classifying spaces
Victor Petrov, Nikita Semenov
In the present article we investigate ordinary and equivariant Rost motives. We provide an equivariant motivic decomposition of the variety X of full flags of a split semisimple al…
Motivic decompositions of twisted flag varieties and representations of Hecke-type algebras
Alexander Neshitov, Victor Petrov, Nikita Semenov +1
Let G be a split semisimple linear algebraic group over a field k0. Let E be a G-torsor over a field extension k of k0. Let h be an algebraic oriented cohomology theory in the sens…
Morava K-theory of twisted flag varieties
Victor Petrov, Nikita Semenov
In the present article we prove some results about the Morava K-theory. In particular, we construct an operation from the Morava K-theory to the Chow theory analogous to the second…
A rational construction of Lie algebras of type E_7
Victor Petrov
We give an explicit construction of Lie algebras of type out of a Lie algebra of type with some restrictions. Up to odd degree extensions, every Lie algebra of type $E_…
Rationally isotropic exceptional projective homogeneous varieties are locally isotropic
Ivan Panin, Victor Petrov
Assume that R is a local regular ring containing an infinite perfect field, or that R is the local ring of a point on a smooth scheme over an infinite field. Let K be the field of…
Shells of twisted flag varieties and the Rost invariant
Skip Garibaldi, Victor Petrov, Nikita Semenov
We introduce two new general methods to compute the Chow motives of twisted flag varieties and settle a 20-year-old conjecture of Markus Rost about the Rost invariant for groups of…
Schubert calculus and singularity theory
Vassily Gorbounov, Victor Petrov
Schubert calculus has been in the intersection of several fast developing areas of mathematics for a long time. Originally invented as the description of the cohomology of homogene…
Grothendieck-Serre conjecture for groups of type F_4 with trivial f_3 invariant
Victor Petrov, Anastasia Stavrova
Let R be a semi-local regular ring containing an infinite perfect field, and let K be the field of fractions of R. Let H be a simple algebraic group of type F_4 over R such that H_…
Grothendieck-Serre conjecture for adjoint groups of types E_6 and E_7 and for certain classical groups
I. Panin, V. Petrov, A. Stavrova
Assume that R is a semi-local regular ring containing an infinite perfect field, or that R is a semi-local ring of several points on a smooth scheme over an infinite field. Let K b…
Invariants, torsion indices and oriented cohomology of complete flags
Baptiste Calmès, Victor Petrov, Kirill Zainoulline
In the present notes we generalize the classical work of Demazure [Invariants symétriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and form…
Tits indices over semilocal rings
V. Petrov, A. Stavrova
We give a simplified proof of Tits' classification of semisimple algebraic groups that remains valid over semilocal rings. In particular, we provide explicit necessary and sufficie…
J-invariant of linear algebraic groups
Victor Petrov, Nikita Semenov, Kirill Zainoulline
Let G be a linear algebraic group over a field F and X be a projective homogeneous G-variety such that G splits over the function field of X. In the present paper we introduce an i…