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A fixed point theorem in Euclidean buildings

Christophe Cornut
From the journal Advances in Geometry

Abstract

We establish a fixed point theoremfor a certain type of non-expandingmaps in Euclidean buildings, which is inspired by a theorem of Laffaille in p-adic Hodge theory [10, Theorem 3.2].

MSC 2010: 52B05

Communicated by: R. Scharlau


Acknowledgement

This work grew out of a collaboration with Marc-Hubert Nicole on G-isocrystals and a related question of Jean-François Dat: what about filtrations? Bruno Klingler provided the enlightening reference [9], Anders Karlsson the proof of his remark, and Guy Rousseau the proof of Proposition 4.

Funding

Grant ANR-10-BLAN-0114 ArShiFo.

Reference

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Received: 2014-7-5
Revised: 2015-11-26
Revised: 2016-3-8
Published Online: 2016-10-13
Published in Print: 2016-10-1

© 2016 by Walter de Gruyter Berlin/Boston

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