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 $\mathbf{G}$ be a reductive Chevalley group scheme (defined over$\mathbb{Z}$). Let $\mathcal{C}$ be a smooth, projective, geometricallyintegral curve over a field $\mathbb{F}$. Let $P$ be a closed point on$\mathcal{C}$. Let $A$ be the ring of functions that are regular outside$\lbrace P \rbrace$. The fraction field $k$ of $A$ has a discrete valuation$\nu=\nu_{P}: k^{\times} \rightarrow \mathbb{Z}$ associated to $P$. In thiswork, we study the action of the group $ \textbf{G}(A)$ of $A$-points of$\mathbf{G}$ on the Bruhat-Tits building$\mathcal{X}=\mathcal{X}(\textbf{G},k,\nu_{P})$ in order to describe thestructure of the orbit space $ \textbf{G}(A)\backslash \mathcal{X}$. We obtainthat this orbit space is the ``gluing'' of a closed connected CW-complex withsome sector chambers. The latter are parametrized by a set depending on thePicard group of $\mathcal{C} \smallsetminus \{P\}$ and on the rank of$\mathbf{G}$. Moreover, we observe that any rational sector face whose tip is aspecial vertex contains a subsector face that embeds into this orbit space.

Arithmetic subgroups of Chevalley group schemes over function fields I: quotients of the Bruhat-Tits building by $\{P\}$-arithmetic subgroups