Algebra & Number Theory
- Algebra Number Theory
- Volume 7, Number 4 (2013), 853-892.
Albanese varieties with modulus over a perfect field
Let be a smooth proper variety over a perfect field of arbitrary characteristic. Let be an effective divisor on with multiplicity. We introduce an Albanese variety of of modulus 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 of modulus and show that can be viewed as a universal quotient of .
As an application we can rephrase Lang’s class field theory of function fields of varieties over finite fields in explicit terms.
Algebra Number Theory, Volume 7, Number 4 (2013), 853-892.
Received: 18 February 2011
Revised: 7 April 2012
Accepted: 17 May 2012
First available in Project Euclid: 20 December 2017
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Russell, Henrik. Albanese varieties with modulus over a perfect field. Algebra Number Theory 7 (2013), no. 4, 853--892. doi:10.2140/ant.2013.7.853. https://projecteuclid.org/euclid.ant/1513729984