Vol. 7, No. 4, 2013

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

Volume 18
Issue 12, 2133–2308
Issue 11, 1945–2131
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
Albanese varieties with modulus over a perfect field

Henrik Russell

Vol. 7 (2013), No. 4, 853–892
Abstract

Let X be a smooth proper variety over a perfect field k of arbitrary characteristic. Let D be an effective divisor on X with multiplicity. We introduce an Albanese variety Alb(X,D) of X of modulus D as a higher-dimensional analogue of the generalized Jacobian of Rosenlicht and Serre with modulus for smooth proper curves. Basing on duality of 1-motives with unipotent part (which are introduced here), we obtain explicit and functorial descriptions of these generalized Albanese varieties and their dual functors.

We define a relative Chow group of zero cycles CH0(X,D) of modulus D and show that Alb(X,D) can be viewed as a universal quotient of CH0(X,D)0.

As an application we can rephrase Lang’s class field theory of function fields of varieties over finite fields in explicit terms.

Keywords
Albanese with modulus, relative Chow group with modulus, geometric class field theory
Mathematical Subject Classification 2010
Primary: 14L10
Secondary: 11G45, 14C15
Milestones
Received: 18 February 2011
Revised: 7 April 2012
Accepted: 17 May 2012
Published: 29 August 2013
Authors
Henrik Russell
Freie Universität Berlin
Mathematik und Informatik
Arnimallee 3
14195 Berlin
Germany