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arXiv · 1305.5057

On lower bounds for cohomology growth in p-adic analytic towers

Steffen Kionke
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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.

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BibTeXRIS

Steffen Kionke. 2014-01-09. On lower bounds for cohomology growth in p-adic analytic towers. https://doi.org/10.1007/s00209-013-1273-3

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