Displaying similar documents to “Ideal class groups, Hilbert’s irreducibility theorem, and integral points of bounded degree on curves”

Gross’ conjecture for extensions ramified over four points of ℙ 1

Po-Yi Huang (2006)

Journal de Théorie des Nombres de Bordeaux

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In this paper, under a mild hypothesis, we prove a conjecture of Gross for the Stickelberger element of the maximal abelian extension over the rational function field unramified outside a set of four degree-one places.

The field-of-norms functor and the Hilbert symbol for higher local fields

Victor Abrashkin, Ruth Jenni (2012)

Journal de Théorie des Nombres de Bordeaux

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The field-of-norms functor is applied to deduce an explicit formula for the Hilbert symbol in the mixed characteristic case from the explicit formula for the Witt symbol in characteristic p > 2 in the context of higher local fields. Is is shown that a “very special case” of this construction gives Vostokov’s explicit formula.

Variations on a theme of Runge: effective determination of integral points on certain varieties

Aaron Levin (2008)

Journal de Théorie des Nombres de Bordeaux

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We consider some variations on the classical method of Runge for effectively determining integral points on certain curves. We first prove a version of Runge’s theorem valid for higher-dimensional varieties, generalizing a uniform version of Runge’s theorem due to Bombieri. We then take up the study of how Runge’s method may be expanded by taking advantage of certain coverings. We prove both a result for arbitrary curves and a more explicit result for superelliptic curves. As an application...