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Cohomological divisibility and point count divisibility

Hélène Esnault·Nicholas M. Katz
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Abstract

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]

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Hélène Esnault, Nicholas M. Katz. 2003-05-10. Cohomological divisibility and point count divisibility. https://arxiv.org/abs/math/0305127

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