April 29, 2024Open Access

Logarithmic geometry and Frobenius

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Abstract

Based on the logarithmic algebraic geometry and the theory of Deligne systems, we define an abelian category of -adic sheaves with weight filtrations on a logarithmic scheme over a finite field, which is similar to the category of variations of mixed Hodge structure. We consider asymptotic behaviors and simple cases of higher direct images of objects of this category. This category is closely related to the monodromy-weight conjecture.

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Katô et al. (Mon,) studied this question.

synapsesocial.com/papers/68e6d2d1b6db64358765016e https://doi.org/https://doi.org/10.48550/arxiv.2404.19183

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