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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Let $F_{\wp}$ be a finite extension of $\mathbb{Q}_p$. By considering partially de Rham families, we establish a Colmez-Greenberg-Stevens formula (on Fontaine-Mazur $\mathcal{L}$-invariants) for (general) $2$-dimensional semi-stable non-crystalline $\mathrm{Gal}(\overline{\mathbb{Q}_p}/F_{\wp})$-representations. As an application, we prove local-global compatibility results for completed cohomology of quaternion Shimura curves, and in particular the equality of Fontaine-Mazur $\mathcal{L}$-invariants and Breuil's $\mathcal{L}$-invariants, in critical case.

\protect \mathcal{L}-invariants, partially de Rham families, and local-global compatibility