A Geometric Proof of Hermite’s Theorem in Function Fields
Journal de Théorie des Nombres de Bordeaux, Volume 29 (2017) no. 3, pp. 799-813.

An important theorem of C. Hermite asserts that any set of algebraic number fields, whose discriminants are bounded in absolute value, must be finite. Properly formulated, a similar theorem holds true for function fields in one variable over a finite constant field. This paper gives a new proof of this result by using an analogue of the geometry of numbers approach due to H. Minkowski in the number field case.

Un théorème important de C. Hermite énonce que tout ensemble de corps de nombres, dont les discriminants sont bornés en valeur absolue, doit être fini. Correctement formulé, un résultat similaire est valable pour des corps de fonctions d’une variable sur un corps de constantes fini. Cet article donne une nouvelle preuve de ce résultat par l’analogie avec l’approche de la « géométrie des nombres » de H. Minkowski dans le cas des corps de nombres.

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DOI: 10.5802/jtnb.1001
Classification: 11N56,  14G42
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Michael Rosen. A Geometric Proof of Hermite’s Theorem in Function Fields. Journal de Théorie des Nombres de Bordeaux, Volume 29 (2017) no. 3, pp. 799-813. doi : 10.5802/jtnb.1001. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1001/

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