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Monodromy of Tate-Linear varieties

  • Livia Grammatica
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Abstract

We answer a question of Chai about the rigidity of Tate-linear subvarieties of π’œg over 𝔽̅p: we show that that a smooth subvariety of a central leaf of π’œg which is Tate-linear at one point is Tate-linear at every point. This is achieved by a careful analysis of the p-adic monodromy groups of Tate-linear varieties, building on recent work of D'Addezio and van Hoften.

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Cite

BibTeXRIS
BibTeX
@misc{grammatica2026monodromy,
  title = {{Monodromy of Tate-Linear varieties}},
  author = {Livia Grammatica},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13827},
  eprint = {2610.13827},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13827},
}
RIS
TY  - UNPB
TI  - Monodromy of Tate-Linear varieties
AU  - Livia Grammatica
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13827
UR  - https://arxiv.org/abs/2610.13827
AB  - We answer a question of Chai about the rigidity of Tate-linear subvarieties of π’œ_g over 𝔽̅_p: we show that that a smooth subvariety of a central leaf of π’œ_g which is Tate-linear at one point is Tate-linear at every point. This is achieved by a careful analysis of the p-adic monodromy groups of Tate-linear varieties, building on recent work of D'Addezio and van Hoften.
ER  -