Year: 2026
Type: preprint
Abstract: We study Galois coinvariants of the geometric étale fundamental group and étale cohomology of varieties over a finitely generated field $k$. We establish finiteness properties of these coinvariants for (possibly infinite) Galois extensions $L/k$ such that $\operatorname{Gal}(L/k)^{\mathrm{ab}}$ has finite exponent. As applications, we obtain finiteness results for $L$-rational torsion points on abelian varieties and étale fundamental groups of arithmetic schemes over number fields.
Source: arXiv (Cornell University)
Author: Steklov, Benjamin
Institution: Goethe University Frankfurt
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7221765077