Vol. 13, No. 6, 2019

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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

Let F be a nonarchimedean local field and let T be a torus over F. With TNR denoting the Néron–Raynaud model of T, a result of Chai and Yu asserts that the model TNR ×OFOFpFm is canonically determined by (Trl(F),Λ) for l m, where Trl(F) = (OFpFl,pFpFl+1,ϵ) with ϵ denoting the natural projection of pFpFl+1 on pFpFl, 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.

parahoric, close local fields
Mathematical Subject Classification 2010
Primary: 22E50
Secondary: 11F70
Received: 6 November 2018
Revised: 16 April 2019
Accepted: 25 May 2019
Published: 18 August 2019
Radhika Ganapathy
School of Mathematics
Tata Institute of Fundamental Research