Common hyperbolic bases for chains of alternating or quadratic lattices
Number Theory
2019-07-02 v5
Abstract
We give a short and purely bilinear proof of the fact that two chains of -elementary lattices with quadratic form or alternating bilinear form over the -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.
Keywords
Cite
@article{arxiv.1808.09504,
title = {Common hyperbolic bases for chains of alternating or quadratic lattices},
author = {Rainer Schulze-Pillot},
journal= {arXiv preprint arXiv:1808.09504},
year = {2019}
}
Comments
6 pages, to appear in Mathematische Annalen. The final publication is available at Springer via https://link.springer.com/journal/208