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The regular inverse Galois problem over fields avoiding a curve
Abstract
Let k0 be a field of characteristic $0$, and let C/k0 be a smooth geometrically integral curve of positive genus with C(k0)=∅. We prove that the regular inverse Galois problem is solvable over every field existentially closed in the class of k0-fields avoiding C, including the curve-excluding fields of Johnson and the author. To this end, we show that for every finite group G, there is a parameter variety over ℚ whose function field admits a regular realization of G without adding points to C. Finally, we establish RIGP over the variety-excluding fields of Szachniewicz and the author, when the excluded variety is a locally closed subvariety of an abelian variety.
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BibTeX
@misc{ye2026regular,
title = {{The regular inverse Galois problem over fields avoiding a curve}},
author = {Jinhe Ye},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19689},
eprint = {2610.19689},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19689},
}
RIS
TY - UNPB
TI - The regular inverse Galois problem over fields avoiding a curve
AU - Jinhe Ye
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19689
UR - https://arxiv.org/abs/2610.19689
AB - Let k_0 be a field of characteristic $0$, and let C/k_0 be a smooth geometrically integral curve of positive genus with C(k_0)=∅. We prove that the regular inverse Galois problem is solvable over every field existentially closed in the class of k_0-fields avoiding C, including the curve-excluding fields of Johnson and the author. To this end, we show that for every finite group G, there is a parameter variety over ℚ whose function field admits a regular realization of G without adding points to C. Finally, we establish RIGP over the variety-excluding fields of Szachniewicz and the author, when the excluded variety is a locally closed subvariety of an abelian variety.
ER -