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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Contributor : Sara Checcoli <>
Submitted on : Wednesday, October 25, 2017 - 2:21:36 PM
Last modification on : Tuesday, July 3, 2018 - 11:38:47 AM

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



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



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