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Tate conjecture for products of Fermat varieties over finite fields

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Abstract

We prove under some assumptions that the Tate conjecture holds for products of Fermat varieties of different degrees. The method is to use a combinatorial property of eigenvalues of geometric Frobenius acting on ℓ-adic étale cohomology.

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Authors and Affiliations

  1. Fakultät Mathematik, Universität Duisburg-Essen, Thea-Leymann-Straße 9, 45127, Essen, Germany

    Rin Sugiyama

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  1. Rin Sugiyama
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Correspondence to Rin Sugiyama.

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The author was supported by JSPS Research Fellowships for Young Scientists.

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Sugiyama, R. Tate conjecture for products of Fermat varieties over finite fields. manuscripta math. 144, 421–438 (2014). https://doi.org/10.1007/s00229-013-0652-8

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  • DOI: https://doi.org/10.1007/s00229-013-0652-8

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