Non-algebraic geometrically trivial cohomology classes over finite fields

Research output: Working paper/PreprintPreprint

Authors

  • Federico Scavia
  • Fumiaki Suzuki

Research Organisations

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Original languageEnglish
Publication statusE-pub ahead of print - 23 Sept 2024

Abstract

We give the first examples of smooth projective varieties $X$ over a finite field $\mathbb{F}$ admitting a non-algebraic torsion $\ell$-adic cohomology class of degree $4$ which vanishes over $\overline{\mathbb{F}}$. We use them to show that two versions of the integral Tate conjecture over $\mathbb{F}$ are not equivalent to one another and that a fundamental exact sequence of Colliot-Th\'el\`ene and Kahn does not necessarily split. Some of our examples have dimension $4$, and are the first known examples of fourfolds with non-vanishing $H^{3}_{\text{nr}}(X,\mathbb{Q}_{2}/\mathbb{Z}_{2}(2))$.

Keywords

    math.AG, 14C25, 14G15, 55R35

Cite this

Non-algebraic geometrically trivial cohomology classes over finite fields. / Scavia, Federico; Suzuki, Fumiaki.
2024.

Research output: Working paper/PreprintPreprint

Scavia, F., & Suzuki, F. (2024). Non-algebraic geometrically trivial cohomology classes over finite fields. Advance online publication.
Scavia F, Suzuki F. Non-algebraic geometrically trivial cohomology classes over finite fields. 2024 Sept 23. Epub 2024 Sept 23.
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