198 citations · 271 across the 17 of their papers we have counts for
19 papers
The Balmer spectrum of Voevodsky motives and pure symbols
Alexander Vishik
In this article we introduce invariants of points of the Balmer spectrum of the Voevodsky motivic category whose values are "light Rost cycle submodules" of the module of pure symb…
Varieties and pure symbols
Alexander Vishik
In this article, we prove that the 2-isotropy of any projective variety is controlled by a pure symbol in the Milnor's K-theory (mod 2) of the flexible closure of the base field. W…
On the Balmer spectrum of the Morel-Voevodsky category
Peng Du, Alexander Vishik
We introduce the Morava-isotropic stable homotopy category and, more generally, the stable homotopy category of an extension . These "local" versions of the Morel-Voevodsky st…
On torsion spaces
Alexander Vishik
The purpose of this note is to construct examples of compact torsion objects of of every -level over an arbitrary field of characteristic different from . We a…
Isotropic and numerical equivalence for Chow groups and Morava K-theories
Alexander Vishik
In this paper we prove the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with -coefficients). This shows…
On isotropic and numerical equivalence of cycles
Alexander Vishik
We study the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with -coefficients). This conjecture is essent…
Torsion motives
Alexander Vishik
In this paper we study Chow motives whose identity map is killed by a natural number. Examples of such objects were constructed by Gorchinskiy-Orlov. We introduce various invariant…
Operations in connective K-theory
Alexander Merkurjev, Alexander Vishik
In this article we classify additive operations in connective K-theory with various torsion-free coefficients. We discover that the answer for the integral case requires understand…
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.
Operations and poly-operations in Algebraic Cobordism
Alexander Vishik
We describe all operations from a theory A^* obtained from Algebraic Cobordism of M.Levine-F.Morel by change of coefficients to any oriented cohomology theory B^* (in the case of a…
Algebraic Cobordism as a module over the Lazard ring
Alexander Vishik
In this paper we study the structure of the Algebraic Cobordism ring of a variety as a module over the Lazard ring, and show that it has relations in positive codimensions. We actu…
Subtle Characteristic Classes
Alexander Smirnov, Alexander Vishik
We construct new subtle Stiefel--Whitney classes of quadratic forms. These classes are much more informative than the ones introduced by Milnor. In particular, they see all the pow…
Symmetric operations for all primes and Steenrod operations in Algebraic Cobordism
Alexander Vishik
In this article we construct Symmetric operations for all primes (previously known only for p=2). These unstable operations are more subtle than the Landweber-Novikov operations, a…
Stable and Unstable operations in Algebraic Cobordism
Alexander Vishik
We describe additive (unstable) operations from a theory A^* obtained from Algebraic Cobordism of M.Levine-F.Morel by change of coefficients to any oriented cohomology theory B^*.…
An exact sequence for Milnor's K-theory with applications to quadratic forms
Dmitry Orlov, Alexander Vishik, Vladimir Voevodsky
We construct a four-term exact sequence which provides information on the kernel and cokernel of the multiplication by a pure symbol in Milnor's K-theory mod 2 of fields of charact…
Koszul duality and Galois cohomology
Leonid Positselski, Alexander Vishik
It it shown that the Bloch-Kato conjecture on the norm residue homomorphism follows from its (partially known) low-degree part under the assumption that…