Algebraic stacks whose number of points over finite fields is a polynomial
| dc.creator | Bogaart, Theo van den | |
| dc.creator | Edixhoven, Bas | |
| dc.date | 2005-05-10 | |
| dc.date | 2008-11-01 | |
| dc.date.accessioned | 2026-07-07T10:14:40Z | |
| dc.date.available | 2026-07-07T10:14:40Z | |
| dc.description | The aim of this article is to investigate the cohomology (l-adic as well as Betti) of schemes, and more generally of certain algebraic stacks, that are proper and smooth over the integers and have the property that there exists a polynomial P with rational coefficients such that for all prime powers q the number of points over the field with q elements is P(q). We prove that for all prime numbers l the l-adic etale cohomology is a direct sum of Tate twists of the trivial representation. Our main tools here are Behrend's Lefschetz trace formula and l-adic Hodge theory. In the last section we investigate the Hodge structure on the Betti cohomology. The motivation for this article comes from applications to certain moduli stacks of curves. | |
| dc.description | 13 pages. Using the first author's results in arXiv:0809.1242, the extra condition that the coarse moduli space is a certain quotient space in the Corollary of the last section of this article has been removed | |
| dc.identifier | https://arxiv.org/abs/math/0505178 | |
| dc.identifier | http://arxiv.org/abs/math/0505178 | |
| dc.identifier | Number Fields and Function Fields- Two Parallel Worlds, Progress in Mathematics, Vol. 239, Geer, Gerard van der; Moonen, Ben J.J.; Schoof, René (Eds.), 2005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172957 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14F20 (Primary); 14H10, 14G15 (Secondary) | |
| dc.title | Algebraic stacks whose number of points over finite fields is a polynomial | |
| dc.type | text |