On lower bounds for cohomology growth in p-adic analytic towers
Group Theory
2017-03-02 v3 Geometric Topology
Number Theory
Abstract
Let p and l be two distinct prime numbers and let G be a group. We study the asymptotic behaviour of the mod-l Betti numbers in p-adic analytic towers of finite index subgroups. If X is a finite l-group of automorphisms of G, our main theorem allows to lift lower bounds for the mod-l cohomology growth in the fixed point group G^X to lower bounds for the growth in G. We give applications to S-arithmetic groups and we also obtain a similar result for cohomology with rational coefficients.
Keywords
Cite
@article{arxiv.1305.5057,
title = {On lower bounds for cohomology growth in p-adic analytic towers},
author = {Steffen Kionke},
journal= {arXiv preprint arXiv:1305.5057},
year = {2017}
}
Comments
14 pages, final version, to appear in Math. Z. (The final publication is available at link.springer.com)