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arXiv · 2502.16974

Logarithmic Tate conjectures over finite fields

Kazuya Kato·Chikara Nakayama·Sampei Usui
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Abstract

We formulate an analogue of Tate conjecture on algebraic cycles, for the log geometry over a finite field. We show that the weight-monodromy conjecture follows from this conjecture and from the semi-simplicity of the Frobenius action. This conjecture suggests the existence of the monodromy cycle which gives the monodromy operator and an action of ${\frak{sl}}(2)$ on the cohomology, and which lives in the world of log motives.

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Kazuya Kato, Chikara Nakayama, Sampei Usui. 2025-02-24. Logarithmic Tate conjectures over finite fields. https://arxiv.org/abs/2502.16974

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