Abstract
Let \({\mathbb{F}}\) be a finite field. The function field analog of Hermite’s theorem says that there are at most finitely many finite separable extensions of \({\mathbb{F}(T)}\) inside a fixed separable closure of \({\mathbb{F}(T)}\) whose discriminant divisors have bounded degree. In this paper we give a field theoretic proof of this result, inspired by a lemma of Faltings for comparing semisimple \({\ell }\)-adic Galois representations.
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Siman Wong’s work is supported in part by NSF Grant DMS-0901506.
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Wong, S. A field theoretic proof of Hermite’s theorem for function fields. Arch. Math. 105, 351–360 (2015). https://doi.org/10.1007/s00013-015-0818-6
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DOI: https://doi.org/10.1007/s00013-015-0818-6