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/

Zendy Plus

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

Zendy Tools

Zendy Open

Let $G$ be the group of rational points of a split connected reductive groupover a nonarchimedean local field of residue characteristic $p$. Let $I$ be apro-$p$ Iwahori subgroup of $G$ and let $R$ be a commutative quasi-Frobeniusring. If $H=R[I\backslash G/I]$ denotes the pro-$p$ Iwahori-Hecke algebra of$G$ over $R$ we clarify the relation between the category of $H$-modules andthe category of $G$-equivariant coefficient systems on the semisimpleBruhat-Tits building of $G$. If $R$ is a field of characteristic zero thisyields alternative proofs of the exactness of the Schneider-Stuhler resolutionand of the Zelevinski conjecture for smooth $G$-representations generated bytheir $I$-invariants. In general, it gives a description of the derivedcategory of $H$-modules in terms of smooth $G$-representations and yields afunctor to generalized $(\varphi,\Gamma)$-modules extending the constructionsof Colmez, Schneider and Vign\'eras.

Coefficient systems on the Bruhat-Tits building and pro-$p$ Iwahori-Hecke modules