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Cohomology of integral structure sheaves for open varieties

  • Xinyu Shao
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Abstract

We study the cohomology of integral structure sheaves for two types of open rigid analytic varieties: complements of divisors in quasi-compact varieties, and partially proper spaces. As applications, we prove a strengthened form of the Hebbarkeitssatz (Riemann's extension theorem), involving the almost vanishing of R1lim, and study pro-étale G-torsors on open varieties.

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Cite

BibTeXRIS
BibTeX
@misc{shao2026cohomology,
  title = {{Cohomology of integral structure sheaves for open varieties}},
  author = {Xinyu Shao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31289},
  eprint = {2610.31289},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31289},
}
RIS
TY  - UNPB
TI  - Cohomology of integral structure sheaves for open varieties
AU  - Xinyu Shao
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31289
UR  - https://arxiv.org/abs/2610.31289
AB  - We study the cohomology of integral structure sheaves for two types of open rigid analytic varieties: complements of divisors in quasi-compact varieties, and partially proper spaces. As applications, we prove a strengthened form of the Hebbarkeitssatz (Riemann's extension theorem), involving the almost vanishing of R^1lim, and study pro-étale G-torsors on open varieties.
ER  -