Algebraic stacks whose number of points over finite fields is a polynomial
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...
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Published in | arXiv.org |
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Main Authors | , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
01.11.2008
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 2331-8422 |