Open Access
Translator Disclaimer
2018 Torsion in the 0-cycle group with modulus
Amalendu Krishna
Algebra Number Theory 12(6): 1431-1469 (2018). DOI: 10.2140/ant.2018.12.1431

Abstract

We show, for a smooth projective variety X over an algebraically closed field k with an effective Cartier divisor D , that the torsion subgroup CH 0 ( X | D ) { l } can be described in terms of a relative étale cohomology for any prime l p = char ( k ) . This extends a classical result of Bloch, on the torsion in the ordinary Chow group, to the modulus setting. We prove the Roitman torsion theorem (including p -torsion) for CH 0 ( X | D ) when D is reduced. We deduce applications to the problem of invariance of the prime-to- p torsion in CH 0 ( X | D ) under an infinitesimal extension of D .

Citation

Download Citation

Amalendu Krishna. "Torsion in the 0-cycle group with modulus." Algebra Number Theory 12 (6) 1431 - 1469, 2018. https://doi.org/10.2140/ant.2018.12.1431

Information

Received: 12 May 2017; Revised: 11 September 2017; Accepted: 15 February 2018; Published: 2018
First available in Project Euclid: 25 October 2018

zbMATH: 06973916
MathSciNet: MR3864203
Digital Object Identifier: 10.2140/ant.2018.12.1431

Subjects:
Primary: 14C25
Secondary: 13F35 , 14F30 , 19F15

Keywords: algebraic K-theory , cycles on singular schemes , Cycles with modulus , étale cohomology

Rights: Copyright © 2018 Mathematical Sciences Publishers

JOURNAL ARTICLE
39 PAGES


SHARE
Vol.12 • No. 6 • 2018
MSP
Back to Top