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Multiplicator freeness for restricted-ramification Galois groups over global function fields

  • Qi Liu
  • Zugan Xing
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Abstract

Let K be a global function field with full constant field 𝔽q, let T be a finite set of finite places, and let ∞ be a distinguished place. We study the maximal pro-β„“ extension of K which is unramified outside T and in which ∞ splits completely. Using factorisation results for β„“-primary idele class characters, we prove that its Galois group is multiplicator-free if β„“ nmid q βˆ’ 1 or T β‰  βˆ…. In particular, if T β‰  βˆ…, the conclusion holds for every prime β„“.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026multiplicator,
  title = {{Multiplicator freeness for restricted-ramification Galois groups over global function fields}},
  author = {Qi Liu and Zugan Xing},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.12240},
  eprint = {2608.12240},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.12240},
}
RIS
TY  - UNPB
TI  - Multiplicator freeness for restricted-ramification Galois groups over global function fields
AU  - Qi Liu
AU  - Zugan Xing
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2608.12240
UR  - https://arxiv.org/abs/2608.12240
AB  - Let K be a global function field with full constant field 𝔽_q, let T be a finite set of finite places, and let ∞ be a distinguished place. We study the maximal pro-β„“ extension of K which is unramified outside T and in which ∞ splits completely. Using factorisation results for β„“-primary idele class characters, we prove that its Galois group is multiplicator-free if β„“ nmid q βˆ’ 1 or T β‰  βˆ…. In particular, if T β‰  βˆ…, the conclusion holds for every prime β„“.
ER  -