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arXiv · 2403.00500

On the height of some generators of galois extensions with big galois group

Jonathan Jenvrin
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Abstract

We study the height of generators of Galois extensions of the rationals having the alternating group $\mathfrak{A}_n$ as Galois group. We prove that if such generators are obtained from certain, albeit classical, constructions, their height tends to infinity as $n$ increases. This provides an analogue of a result by Amoroso, originally established for the symmetric group.

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Jonathan Jenvrin. 2024-03-01. On the height of some generators of galois extensions with big galois group. https://arxiv.org/abs/2403.00500

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