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arXiv · 2610.16760

Galois coinvariants and fundamental groups of arithmetic schemes

Benjamin Steklov
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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 an application, we obtain a finiteness result for étale fundamental groups of arithmetic schemes over number fields.

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Benjamin Steklov. 2026-10-12. Galois coinvariants and fundamental groups of arithmetic schemes. https://arxiv.org/abs/2610.16760

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