Tchebotarev theorems for function fields
Number Theory
2013-01-10 v1
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.
Keywords
Cite
@article{arxiv.1301.1815,
title = {Tchebotarev theorems for function fields},
author = {Sara Checcoli and Pierre Dèbes},
journal= {arXiv preprint arXiv:1301.1815},
year = {2013}
}