Weil-Moore anima — Draconitic Research

Abstract

The Weil group of a number field is a refinement of its absolute Galois group arising from class field theory. The passage from Galois to Weil is important in several places in number theory. However, we will argue that while from the Galois perspective, a number field is a ``K(π,1)'', from the Weil perspective it is not. Thus we are led to further refine the Weil group, by constructing an object, the Weil-Moore anima, which has the Weil group as its fundamental group, but with nontrivial higher homotopy groups. Our motivation is that the cohomological properties of Weil-Moore anima are in several ways nicer than those of the Weil or Galois groups.

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BibTeX RIS

BibTeX

@misc{clausen2026weilmoore,
  title = {{Weil-Moore anima}},
  author = {Dustin Clausen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.11950},
  eprint = {2605.11950},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.11950},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Weil-Moore anima
AU  - Dustin Clausen
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2605.11950
UR  - https://arxiv.org/abs/2605.11950
AB  - The Weil group of a number field is a refinement of its absolute Galois group arising from class field theory. The passage from Galois to Weil is important in several places in number theory. However, we will argue that while from the Galois perspective, a number field is a ``K(π,1)'', from the Weil perspective it is not. Thus we are led to further refine the Weil group, by constructing an object, the Weil-Moore anima, which has the Weil group as its fundamental group, but with nontrivial higher homotopy groups. Our motivation is that the cohomological properties of Weil-Moore anima are in several ways nicer than those of the Weil or Galois groups.
ER  -

Abstract

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