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 $k$ be an algebraically closed field of characteristic $p$ and let $X$the projective line over $k$ with three points removed. We investigate whichfinite groups $G$ can arise as the monodromy group of finite \'{e}tale coversof $X$ that are tamely ramified over the three removed points. This providesnew information about the tame fundamental group of the projective line. Inparticular, we show that for each prime $p\ge 5$, there are families of tamelyramified covers with monodromy the symmetric group $S_n$ or alternating group$A_n$ for infinitely many $n$. These covers come from the moduli spaces ofelliptic curves with $PSL_2(\mathbb{F}_\ell)$-structure, and the analysis useswork of Bourgain, Gamburd, and Sarnak, and adapts work of Meiri and Puder,about Markoff triples modulo $\ell$.

Tamely Ramified Covers of the Projective Line with Alternating and Symmetric Monodromy