Vol. 12, No. 6, 2018

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

Volume 14
Issue 8, 2001–2294
Issue 7, 1669–1999
Issue 6, 1331–1667
Issue 5, 1055–1329
Issue 4, 815–1054
Issue 3, 545–813
Issue 2, 275–544
Issue 1, 1–274

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
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
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