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On the notion of ๐”ธ1-coverings

  • Marco Giustetto
  • Thor Wittich
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Abstract

We introduce the notion of ๐”ธ1-n-coverings and begin the development of their theory over an arbitrary base scheme S, in analogy to that of higher coverings in an โˆž-topos. We show that for n=0, our notion recovers Morel's ๐”ธ1-coverings between simplicial sheaves. Under suitable assumptions, we then provide a Galois-theoretic classification of ๐”ธ1-n-coverings. Finally, we answer a question of Morel concerning a geometric criterion for ๐”ธ1-coverings in the negative.

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Cite

BibTeXRIS
BibTeX
@misc{giustetto2026notion,
  title = {{On the notion of $\mathbbA^1$-coverings}},
  author = {Marco Giustetto and Thor Wittich},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26345},
  eprint = {2610.26345},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26345},
}
RIS
TY  - UNPB
TI  - On the notion of ๐”ธ^1-coverings
AU  - Marco Giustetto
AU  - Thor Wittich
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26345
UR  - https://arxiv.org/abs/2610.26345
AB  - We introduce the notion of ๐”ธ^1-n-coverings and begin the development of their theory over an arbitrary base scheme S, in analogy to that of higher coverings in an โˆž-topos. We show that for n=0, our notion recovers Morel's ๐”ธ^1-coverings between simplicial sheaves. Under suitable assumptions, we then provide a Galois-theoretic classification of ๐”ธ^1-n-coverings. Finally, we answer a question of Morel concerning a geometric criterion for ๐”ธ^1-coverings in the negative.
ER  -