Cohomological divisibility and point count divisibility

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We show that Ax-Katz divisibility on the number of rational points of a variety defined over a finite field by equations of low degrees comes from divisibility of the eigenvalues of the Frobenius action of the $\ell$-adic cohomology with compact supports. This completes the motivc picture, as we knew already that in characteristic 0, the Hodge type was the expected one. [version 2 as the title contained a typo..., else no changes]
10 pages, latex

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Number Theory, Algebraic Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/67410

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0305127
 http://arxiv.org/abs/math/0305127

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arXiv