Logarithmic Tate conjectures over finite fields

Fuente: arXiv
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Autores principales: Kato, Kazuya, Nakayama, Chikara, Usui, Sampei
Formato: Preprint
Publicado: 2025
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author Kato, Kazuya
Nakayama, Chikara
Usui, Sampei
author_facet Kato, Kazuya
Nakayama, Chikara
Usui, Sampei
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2502_16974
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Logarithmic Tate conjectures over finite fields
Kato, Kazuya
Nakayama, Chikara
Usui, Sampei
Algebraic Geometry
Primary 14A21, Secondary 14F20, 19E15
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.
title Logarithmic Tate conjectures over finite fields
topic Algebraic Geometry
Primary 14A21, Secondary 14F20, 19E15
url https://arxiv.org/abs/2502.16974