Tchebotarev theorems for function fields

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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Article dans une revue
Journal of Algebra, Elsevier, 2016, 446, pp.346-372
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https://hal.archives-ouvertes.fr/hal-01623558
Contributeur : Sara Checcoli <>
Soumis le : mercredi 25 octobre 2017 - 14:21:36
Dernière modification le : jeudi 11 janvier 2018 - 06:12:18

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  • HAL Id : hal-01623558, version 1
  • ARXIV : 1301.1815

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Sara Checcoli, Pierre Dèbes. Tchebotarev theorems for function fields. Journal of Algebra, Elsevier, 2016, 446, pp.346-372. 〈hal-01623558〉

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