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arXiv · 1801.07173

Abelian capitulation of ray class groups

Jean-François Jaulent
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Abstract

Building on Bosca's method, we extend to tame ray class groups the results on capitulation of ideals of a number field by composition with abelian extensions of a subfield first studied by Gras. More precisely, for every extension of number fields K/k, where at least one infinite place splits completely, and every squarefree divisor m of K, we prove that there exist infinitely many abelian extensions F/k such that the ray class group mod m of K capitulates in KF. As a consequence we generalize to tame ray class groups the results of Kurihara on triviality of class groups for maximal abelian pro-extensions of totally real number fields.

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Jean-François Jaulent. 2018-01-19. Abelian capitulation of ray class groups. https://arxiv.org/abs/1801.07173

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