Congruences of parahoric group schemes

Ganapathy, Radhika

doi:10.2140/ant.2019.13.1475

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Congruences of parahoric group schemes

Radhika Ganapathy

Vol. 13 (2019), No. 6, 1475–1499

DOI: 10.2140/ant.2019.13.1475

Abstract

Let $F$ be a nonarchimedean local field and let $T$ be a torus over $F$ . With $T^{N R}$ denoting the Néron–Raynaud model of $T$ , a result of Chai and Yu asserts that the model $T^{N R} \times_{O_{F}} O_{F} ∕ p_{F}^{m}$ is canonically determined by $({T r}_{l} (F), Λ)$ for $l ≫ m$ , where ${T r}_{l} (F) = (O_{F} ∕ p_{F}^{l}, p_{F} ∕ p_{F}^{l + 1}, ϵ)$ with $ϵ$ denoting the natural projection of $p_{F} ∕ p_{F}^{l + 1}$ on $p_{F} ∕ p_{F}^{l}$ , 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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Keywords

parahoric, close local fields

Mathematical Subject Classification 2010

Primary: 22E50

Secondary: 11F70

Milestones

Received: 6 November 2018

Revised: 16 April 2019

Accepted: 25 May 2019

Published: 18 August 2019

Authors

Radhika Ganapathy
School of Mathematics Tata Institute of Fundamental Research Mumbai India

Vol. 13, No. 6, 2019