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arXiv · 2610.40017

Hilbertian Fields and Profinite Iterated Monodromy Groups Over Transcendental Elements with Specializations of Infinite Index

Daniel Gotshall
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Abstract

Given a field $L$ and polynomial $f(x)/L$, one can consider the indices of the profinite iterated monodromy groups formed over the ground field within the profinite iterated monodromy groups over elements transcendental over $L$. For any countable Hilbertian field $k$, we show random Galois fixed field extensions almost surely make the indices infinite over all ground field elements, with certain conditions on $f(x)$. This is a generalization of a result in arXiv:2012.03076 by Dittmann and Kadets.

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BibTeXRIS

Daniel Gotshall. 2026-10-29. Hilbertian Fields and Profinite Iterated Monodromy Groups Over Transcendental Elements with Specializations of Infinite Index. https://arxiv.org/abs/2610.40017

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