All Outputs (12)

Isotropic and numerical equivalence for Chow groups and Morava K-theories (2024)
Journal Article

In this paper we prove the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with Fp-coefficients). This shows that Isotropic Chow motives coincide with Numerical Chow motives. In particular,... Read More about Isotropic and numerical equivalence for Chow groups and Morava K-theories.

Operations in connective K-theory (2023)
Journal Article

We classify additive operations in connective K-theory with various torsion-free coefficients. We discover that the answer for the integral case requires understanding of the ˆZ case. Moreover, although integral additive operations are topologically... Read More about Operations in connective K-theory.

Torsion Motives (2023)
Journal Article

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 [10]. We introduce various invariants of torsion motives, in particular, the p-level. We show that th... Read More about Torsion Motives.

On isotropic and numerical equivalence of cycles (2022)
Journal Article

We study the conjecture claiming that, over a flexible field, isotropic Chow groups coincide with numerical Chow groups (with Fp-coefficients). This conjecture is essential for understanding the structure of the isotropic motivic category and that of... Read More about On isotropic and numerical equivalence of cycles.

ISOTROPIC MOTIVES (2020)
Journal Article

In this article we introduce the local versions of the Voevodsky category of motives with Fp coefficients over a field k, parameterized by finitely-generated extensions of k. We introduce the, so-called, flexible fields, passage to which is conservat... Read More about ISOTROPIC MOTIVES.

Operations and poly-operations in algebraic cobordism (2020)
Journal Article

© 2020 Elsevier Inc. In the case of a field of characteristic zero, we describe all operations (including non-additive ones) from a theory A⁎ obtained from Algebraic Cobordism Ω⁎ of M. Levine-F. Morel by change of coefficients to any oriented cohomol... Read More about Operations and poly-operations in algebraic cobordism.

Affine quadrics and the Picard group of the motivic category (2019)
Journal Article

In this paper we study the subgroup of the Picard group of Voevodsky's category of geometric motives DMgm(k; Z/2) generated by the reduced motives of affine quadrics. Our main tools here are the functors of Bachmann [On the invertibility of motives o... Read More about Affine quadrics and the Picard group of the motivic category.

Stable and unstable operations in algebraic cobordism (2019)
Journal Article

© 2019 Société Mathématique de France. Tous droits réservés - We describe additive (unstable) operations from a theory A* obtained from the Levine-Morel algebraic cobordism by change of coefficients to any oriented cohomology theory B* (over a field... Read More about Stable and unstable operations in algebraic cobordism.

Rost nilpotence and free theories (2018)
Journal Article

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 varieties in the category of h_*-motives. Examples of such theories are... Read More about Rost nilpotence and free theories.

Motivic equivalence of affine quadrics (2018)
Journal Article

In this article we show that the motive of an affine quadric {q=1} determines the respective quadratic form.

Symmetric operations for all primes and Steenrod operations in Algebraic Cobordism (2016)
Journal Article

Algebraic Cobordism as a module over the Lazard ring (2015)
Journal Article

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 actually prove the stronger graded version. This extends the result of Lev... Read More about Algebraic Cobordism as a module over the Lazard ring.