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- W3212920220 abstract "Let $p$ be a prime, and let $K$ be a finite extension of $mathbf{Q}_p$, with absolute Galois group $cal{G}_K$. Let $pi$ be a uniformizer of $K$ and let $K_infty$ be the Kummer extension obtained by adjoining to $K$ a system of compatible $p^n$-th roots of $pi$, for all $n$, and let $L$ be the Galois closure of $K_infty$. Using these extensions, Caruso has constructed 'etale $(varphi,tau)$-modules, which classify $p$-adic Galois representations of $K$. In this paper, we use locally analytic vectors and theories of families of $varphi$-modules over Robba rings to prove the overconvergence of $(varphi,tau)$-modules in families. As examples, we also compute some explicit families of $(varphi,tau)$-modules in some simple cases." @default.
- W3212920220 created "2021-11-22" @default.
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- W3212920220 creator A5017817682 @default.
- W3212920220 date "2021-11-16" @default.
- W3212920220 modified "2023-09-27" @default.
- W3212920220 title "Families of Galois representations and $(varphi, tau)$-modules" @default.
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