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A fully faithful p-adic Riemann--Hilbert functor for filtered coherent D-modules

  • Finn Wiersig
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Abstract

We prove that the solution functor from bounded good filtered complexes of coherent D-modules on a smooth rigid-analytic variety to modules over the positive almost de Rham period sheaf is fully faithful. On filtered vector bundles with flat connection satisfying Griffiths transversality, the construction recovers, up to duality and extension of scalars, Scholze's horizontal sections functor. As an application, we obtain a notion of de Rham Zariski-constructible sheaves, generalising the classical notion of de Rham local systems.

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Cite

BibTeXRIS
BibTeX
@misc{wiersig2026fully,
  title = {{A fully faithful p-adic Riemann--Hilbert functor for filtered coherent D-modules}},
  author = {Finn Wiersig},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24123},
  eprint = {2609.24123},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24123},
}
RIS
TY  - UNPB
TI  - A fully faithful p-adic Riemann--Hilbert functor for filtered coherent D-modules
AU  - Finn Wiersig
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24123
UR  - https://arxiv.org/abs/2609.24123
AB  - We prove that the solution functor from bounded good filtered complexes of coherent D-modules on a smooth rigid-analytic variety to modules over the positive almost de Rham period sheaf is fully faithful. On filtered vector bundles with flat connection satisfying Griffiths transversality, the construction recovers, up to duality and extension of scalars, Scholze's horizontal sections functor. As an application, we obtain a notion of de Rham Zariski-constructible sheaves, generalising the classical notion of de Rham local systems.
ER  -