Vol. 12, No. 6, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 10, 1767–1943
Issue 9, 1589–1766
Issue 8, 1403–1587
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
Torsion in the 0-cycle group with modulus

Amalendu Krishna

Vol. 12 (2018), No. 6, 1431–1469
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 CH0(X|D){l} can be described in terms of a relative étale cohomology for any prime lp = 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 CH0(X|D) when D is reduced. We deduce applications to the problem of invariance of the prime-to-p torsion in CH0(X|D) under an infinitesimal extension of D.

Keywords
Cycles with modulus, cycles on singular schemes, algebraic K-theory, étale cohomology
Mathematical Subject Classification 2010
Primary: 14C25
Secondary: 13F35, 14F30, 19F15
Milestones
Received: 12 May 2017
Revised: 11 September 2017
Accepted: 15 February 2018
Published: 6 October 2018
Authors
Amalendu Krishna
School of Mathematics
Tata Institute of Fundamental Research
Mumbai
India