23 citations · 42 across the 10 of their papers we have counts for
13 papers
A numerical invariant for linear representations of finite groups
Nikita A. Karpenko, Zinovy Reichstein
We study the notion of essential dimension for a linear representation of a finite group. In characteristic zero we relate it to the canonical dimension of certain products of Weil…
Motivic decomposition of compactifications of certain group varieties
Nikita A. Karpenko, Alexander S. Merkurjev
Let D be a central simple algebra of prime degree over a field and let E be an SL_1(D)-torsor. We determine the complete motivic decomposition of certain compactifications of E. We…
Unitary grassmannians
Nikita A. Karpenko
We study projective homogeneous varieties under an action of a projective unitary group (of outer type). We are especially interested in the case of (unitary) grassmannians of tota…
On standard norm varieties
Nikita A. Karpenko, Alexander S. Merkurjev
Let be a prime integer and a field of characteristic 0. Let be the {\em norm variety} of a symbol in the Galois cohomology group (for some…
Incompressibility of orthogonal grassmannians
Nikita A. Karpenko
We prove the following conjecture due to Bryant Mathews (2008). Let Q be the orthogonal grassmannian of totally isotropic i-planes of a non-degenerate quadratic form q over an arbi…
Incompressibility of quadratic Weil transfer of generalized Severi-Brauer varieties
Nikita A. Karpenko
Let X be the variety obtained by the Weil transfer with respect to a quadratic separable field extension of a generalized Severi-Brauer variety. We study (and, in some cases, deter…