4 papers
Isotropic motives
Alexander Vishik
In this article we introduce the local versions of the Voevodsky category of motives with Z/p-coefficients over a field k, parameterized by finitely-generated extensions of k. We i…
Rost nilpotence and free theories
Stefan Gille, Alexander Vishik
We introduce coherent cohomology theories h_* and prove that if such a theory is moreover generically constant then the Rost nilpotence principle holds for projective homogeneous v…
Affine quadrics and the Picard group of the motivic category
Alexander Vishik
In this article we study the subgroup of the Picard group of Voevodsky's category of geometric motives generated by the reduced motives of affine quadrics. Our main tools here are…
Motivic equivalence of affine quadrics
Tom Bachmann, Alexander Vishik
In this article we show that the motive of an affine quadric {q = 1} determines the respective quadratic form.