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PreprintarXiv licencearXiv

The Hodge-to-de Rham spectral sequence can be arbitrarily non-degenerate in positive characteristic

  • Kehao Cheng
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Abstract

There is a long tradition of constructing smooth projective varieties in positive characteristic with non-degenerate Hodge-to-de Rham spectral sequences. In this paper, we show that for any n≥ 1 and any spot $(i, j)$ on the En-page, except for the cases where the differential is forced to be zero for trivial reasons, there exists a smooth projective variety whose Hodge-to-de Rham spectral sequence has a non-zero differential with source Eni, j. Our construction is inspired by constructions of nilmanifolds in complex geometry and can be regarded as a positive characteristic analogue.

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Cite

BibTeXRIS
BibTeX
@misc{cheng2026hodgetode,
  title = {{The Hodge-to-de Rham spectral sequence can be arbitrarily non-degenerate in positive characteristic}},
  author = {Kehao Cheng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35243},
  eprint = {2610.35243},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35243},
}
RIS
TY  - UNPB
TI  - The Hodge-to-de Rham spectral sequence can be arbitrarily non-degenerate in positive characteristic
AU  - Kehao Cheng
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35243
UR  - https://arxiv.org/abs/2610.35243
AB  - There is a long tradition of constructing smooth projective varieties in positive characteristic with non-degenerate Hodge-to-de Rham spectral sequences. In this paper, we show that for any n≥ 1 and any spot $(i, j)$ on the E_n-page, except for the cases where the differential is forced to be zero for trivial reasons, there exists a smooth projective variety whose Hodge-to-de Rham spectral sequence has a non-zero differential with source E_n^i, j. Our construction is inspired by constructions of nilmanifolds in complex geometry and can be regarded as a positive characteristic analogue.
ER  -