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PreprintarXiv licencearXiv

Plectic Lie Algebra Action on Hilbert modular varieties

  • Yuanyang Jiang
  • Lue Pan
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Abstract

We construct some part of the plectic Galois action on the locally analytic p-adically completed cohomology of Hilbert modular varieties, predicted by the plectic conjecture of Nekovář-Scholl. As a byproduct, we prove a vanishing result for the completed cohomology of Hilbert modular varieties below middle degree. To do this, we make use of the partial Sen operators constructed earlier by a geometric method.

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Cite

BibTeXRIS
BibTeX
@misc{jiang2026plectic,
  title = {{Plectic Lie Algebra Action on Hilbert modular varieties}},
  author = {Yuanyang Jiang and Lue Pan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34465},
  eprint = {2609.34465},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34465},
}
RIS
TY  - UNPB
TI  - Plectic Lie Algebra Action on Hilbert modular varieties
AU  - Yuanyang Jiang
AU  - Lue Pan
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34465
UR  - https://arxiv.org/abs/2609.34465
AB  - We construct some part of the plectic Galois action on the locally analytic p-adically completed cohomology of Hilbert modular varieties, predicted by the plectic conjecture of Nekovář-Scholl. As a byproduct, we prove a vanishing result for the completed cohomology of Hilbert modular varieties below middle degree. To do this, we make use of the partial Sen operators constructed earlier by a geometric method.
ER  -