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Michael Rosen
A Geometric Proof of Hermite’s Theorem in Function Fields
Journal de théorie des nombres de Bordeaux, 29 no. 3 (2017), p. 799-813, doi: 10.5802/jtnb.1001
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Class. Math.: 11N56, 14G42

Résumé - Abstract

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.

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