On 0-cycles with modulus

Krishna, Amalendu

doi:10.2140/ant.2015.9.2397

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On 0-cycles with modulus

Amalendu Krishna

Vol. 9 (2015), No. 10, 2397–2415

DOI: 10.2140/ant.2015.9.2397

Abstract

Given a nonsingular surface $X$ over a field and an effective Cartier divisor $D$ , we provide an exact sequence connecting CH $_{0} (X, D)$ and the relative $K$ -group $K_{0} (X, D)$ . We use this exact sequence to answer a question of Kerz and Saito whenever $X$ is a resolution of singularities of a normal surface. This exact sequence and two vanishing theorems are used to show that the localization sequence for ordinary Chow groups does not extend to Chow groups with modulus. This in turn shows that the additive Chow groups of 0-cycles on smooth projective schemes cannot always be represented as reciprocity functors.

Keywords

algebraic cycles, modulus condition, $K$-theory

Mathematical Subject Classification 2010

Primary: 14C25

Secondary: 14F30, 14G40

Milestones

Received: 2 June 2015

Revised: 16 September 2015

Accepted: 9 November 2015

Published: 16 December 2015

Authors

Amalendu Krishna
School of Mathematics Tata Institute of Fundamental Research 1 Homi Bhabha Road, Colaba Mumbai 400005 India

Vol. 9, No. 10, 2015