Common hyperbolic bases for chains of alternating or quadratic lattices

Abstract

We give a short and purely bilinear proof of the fact that two chains of $p$-elementary lattices with quadratic form or alternating bilinear form over the $p$-adic integers ore more generally over a complete discrete valuation ring have common hyperbolic bases. This fact, which is useful for the study of Bruhat-Tits buildings, has been proven before with different methods by Abramenko and Nebe and by Frisch.

arXiv comment6 pages, to appear in Mathematische Annalen. The final publication is available at Springer via https://link.springer.com/journal/208

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