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Cohomology of $(\varphi, \tau)$-modules

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arxiv 2402.02492 v3 pith:PCBI3D32 submitted 2024-02-04 math.NT

Hui Gao , Luming Zhao This is my paper · ORCID
classification math.NT
keywords cohomologycasemodulesvarphiadvancesanalyticaxiomaticconstruct
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abstract

We construct cohomology theories for $(\varphi, \tau)$-modules, and study their relation with cohomology of $(\varphi, \Gamma)$-modules, as well as Galois cohomology. Our method is axiomatic, and can treat the \'etale case, the overconvergent case, and the rigid-overconvergent case simultaneously. We use recent advances in locally analytic cohomology as a key ingredient.

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  1. Multivariable period rings of $p$-adic false Tate curve extension

    math.NT 2025-05 conditional novelty 6.0 of 10

    The paper constructs multivariable period rings for p-adic false Tate curve extensions and shows they bridge (φ,Γ)-modules and (φ,τ)-modules in both categorical and cohomological settings.

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