Work

Nisnevich Descent Fails for 0-cycles With Modulus

Year: 2025

Type: article

Abstract: We show that, contrary to the ordinary Chow groups, the canonical map from the Chow group of 0-cycles with modulus on a $d$-dimensional smooth variety $X$ with an effective divisor $D$ over a field to the $(2d,d)$-th Nisnevich motivic cohomology of $X$ relative to $D$ is not always an isomorphism. This is achieved by showing that the degree zero part of the motivic cohomology with modulus over a finite field is isomorphic to the geometric part of an abelian étale fundamental group with modulus.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf134

Authors: Rahul Gupta, Amalendu Krishna

Institutions: Homi Bhabha National Institute, Institute of Mathematical Sciences, University of California, Santa Barbara

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,534

OpenAlex ID: W4410730124