23 citations · 108 across the 15 of their papers we have counts for
19 papers
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 -…
Applications of the Morava -theory to algebraic groups
Pavel Sechin, Nikita Semenov
In the present article we discuss an approach to cohomological invariants of algebraic groups over fields of characteristic zero based on the Morava -theories, which are general…
Hasse principle for Rost motives
Mikhail Borovoi, Nikita Semenov, Maksim Zhykhovich
We prove a Hasse principle for binary direct summands of the Chow motive of a smooth projective quadric Q over a number field F. Besides, we show that such summands are twists of R…
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…