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].
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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