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arXiv · 1301.1815

Tchebotarev theorems for function fields

Sara Checcoli·Pierre Dèbes
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Abstract

We prove Tchebotarev type theorems for function field extensions over various base fields: number fields, finite fields, p-adic fields, PAC fields, etc. The Tchebotarev conclusion - existence of appropriate cyclic residue extensions - also compares to the Hilbert specialization property. It is more local but holds in more situations and extends to infinite extensions. For a function field extension satisfying the Tchebotarev conclusion, the exponent of the Galois group is bounded by the l.c.m. of the local specialization degrees. Further local-global questions arise for which we provide answers, examples and counter-examples.

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Sara Checcoli, Pierre Dèbes. 2013-01-09. Tchebotarev theorems for function fields. https://arxiv.org/abs/1301.1815

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