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Galois coinvariants and fundamental groups of arithmetic schemes
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 Gal(L/k)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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BibTeX
@misc{steklov2026galois,
title = {{Galois coinvariants and fundamental groups of arithmetic schemes}},
author = {Benjamin Steklov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16760},
eprint = {2610.16760},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16760},
}
RIS
TY - UNPB
TI - Galois coinvariants and fundamental groups of arithmetic schemes
AU - Benjamin Steklov
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16760
UR - https://arxiv.org/abs/2610.16760
AB - 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 Gal(L/k)^ab has finite exponent. As an application, we obtain a finiteness result for étale fundamental groups of arithmetic schemes over number fields.
ER -