English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $p$ be a prime, let $K$ be a complete discrete valuation field ofcharacteristic $0$ with a perfect residue field of characteristic $p$, and let$G_K$ be the Galois group. Let $\pi$ be a fixed uniformizer of $K$, let$K_\infty$ be the extension by adjoining to $K$ a system of compatible $p^n$-throots of $\pi$ for all $n$, and let $L$ be the Galois closure of $K_\infty$.Using these field extensions, Caruso constructs the $(\varphi, \tau)$-modules,which classify $p$-adic Galois representations of $G_K$. In this paper, westudy locally analytic vectors in some period rings with respect to the$p$-adic Lie group $\mathrm{Gal}(L/K)$, in the spirit of the work by Berger andColmez. Using these locally analytic vectors, and using the classicaloverconvergent $(\varphi, \Gamma)$-modules, we can establish theoverconvergence property of the $(\varphi, \tau)$-modules.

Locally analytic vectors and overconvergent $(\varphi, \tau)$-modules