Vol. 7, No. 4, 2013

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

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

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
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
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