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Galois cohomology of $p$-adic fields and $(\varphi, \tau)$-modules
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abstract
We construct various explicit Herr complexes that compute the Galois cohomology of a $p$-adic representation of the absolute Galois group of a complete discrete valuation field of characteristic $0$ with a perfect residue field of characteristic $p$, using the associated $(\varphi,\tau)$-modules (defined by Xavier Caruso), instead of $(\varphi,\Gamma)$-modules. We also give an application to $p$-divisible groups.
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Cited by 1 Pith paper
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Multivariable period rings of $p$-adic false Tate curve extension
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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