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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We relate the singularities of a scheme $X$ to the asymptotics of the numberof points of $X$ over finite rings. This gives a partial answer to a questionof Mustata. We use this result to count representations of arithmetic lattices.More precisely, if $\Gamma$ is an arithmetic lattice whose $\mathbb{Q}$-rank isgreater than one, let $r_n(\Gamma)$ be the number of irreducible$n$-dimensional representations of $\Gamma$ up to isomorphism. We prove thatthere is a constant $C$ (for example, $C=746$ suffices) such that$r_n(\Gamma)=O(n^C)$ for every such $\Gamma$. This answers a question of Larsenand Lubotzky.

Counting points of schemes over finite rings and counting representations of arithmetic lattices