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arXiv · 1805.05697

Congruences of parahoric group schemes

Radhika Ganapathy
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Abstract

Let $F$ be a non-archimedean local field and let $T$ be a torus over $F$. With $\cT^{NR}$ denoting the Néron-Raynaud model of $T$, a result of Chai and Yu asserts that the model $\cT^{NR} \times_{\fO_F} \fO_F/\fp_F^m$ is canonically determined by $(\Tr_l(F), Λ)$ for $l>>m$, where $\Tr_l(F) = (\fO_F/\fp_F^l, \fp_F/\fp_F^{l+1}, ε)$ with $ε$ denoting the natural projection of $\fp_F/\fp_F^{l+1}$ on $\fp_F/\fp_F^l$, and $Λ:=X_*(T)$. In this article we prove an analogous result for parahoric group schemes attached to facets in the Bruhat-Tits building of a connected reductive group over $F$.

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Radhika Ganapathy. 2019-05-27. Congruences of parahoric group schemes. https://doi.org/10.2140/ant.2019.13.1475

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