5 citations · 6 across the 7 of their papers we have counts for
8 papers
Motives, cohomological invariants and the Freudenthal magic square
Nikita Geldhauser, Alexander Henke, Maksim Zhykhovich
We investigate cohomological invariants and motivic invariants of semisimple algebraic groups arising in the Freudenthal magic square. Besides, we show that if the Rost invariant o…
-invariant of linear algebraic groups of outer type
Nikita Geldhauser, Maksim Zhykhovich
We extend the notion of the -invariant to arbitrary semisimple linear algebraic groups and provide complete decompositions for the normed Chow motives of all generically quasi-s…
The J-invariant over splitting fields of Tits algebras
Maksim Zhykhovich
We describe the J-invariant of a semi-simple algebraic group G over a generic splitting field of a Tits algebra of G in terms of the J-invariant over a base field.
Critical varieties and motivic equivalence for algebras with involution
Charles De Clercq, Anne Quéguiner-Mathieu, Maksim Zhykhovich
Motivic equivalence for algebraic groups was recently introduced in [9], where a characterization of motivic equivalent groups in terms of higher Tits indexes is given. As a conseq…
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…
Integral motives, relative Krull-Schmidt principle, and Maranda-type theorems
Nikita Semenov, Maksim Zhykhovich
In the present article we investigate properties of the category of the integral Grothendieck-Chow motives over a field. We discuss the Krull-Schmidt principle for integral motives…
Decompositions of motives of generalized Severi-Brauer varieties
Maksim Zhykhovich
Let p be a positive prime number and X be a Severi-Brauer variety of a central division algebra D of degree p^n, with n>0. We describe all shifts of the motive of X in the complete…
Isotropy of unitary involutions
Nikita Karpenko, Maksim Zhykhovich
We prove the so-called Unitary Isotropy Theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic invol…