p-adic and Motivic Measure on Artin n-stacks
Canadian journal of mathematics, Tome 67 (2015) no. 6, pp. 1219-1246
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We define a notion of $p$ -adic measure on Artin $n$ -stacks that are of strongly finite type over the ring of $p$ -adic integers. $p$ -adic measure on schemes can be evaluated by counting points on the reduction of the scheme modulo ${{p}^{n}}$ . We show that an analogous construction works in the case of Artin stacks as well if we count the points using the counting measure defined by Toën. As a consequence, we obtain the result that the Poincaré and Serre series of such stacks are rational functions, thus extending Denef's result for varieties. Finally, using motivic integration we show that as $p$ varies, the rationality of the Serre series of an Artin stack defined over the integers is uniform with respect to $p$ .
Mots-clés :
14E18, 14A20, p-adic integration, motivic integration, Artin stacks
Balwe, Chetan. p-adic and Motivic Measure on Artin n-stacks. Canadian journal of mathematics, Tome 67 (2015) no. 6, pp. 1219-1246. doi: 10.4153/CJM-2014-021-7
@article{10_4153_CJM_2014_021_7,
author = {Balwe, Chetan},
title = {p-adic and {Motivic} {Measure} on {Artin} n-stacks},
journal = {Canadian journal of mathematics},
pages = {1219--1246},
year = {2015},
volume = {67},
number = {6},
doi = {10.4153/CJM-2014-021-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2014-021-7/}
}
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