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The arithmetic de Rham stack

  • Junhui Qin
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Abstract

We define and study the arithmetic de Rham stack Xarith of a scheme X over a field of characteristic p, and analyze its relation with related stacks such as the Hyodo--Kato stack. We show that Xarith gives a stack-theoretic approach to rigid cohomology and its coefficients, known as overconvergent isocrystals and arithmetic D-modules, which avoids the long-standing problem of frame-choosing in earlier approaches. We finally give some arithmetic applications of our formalism, such as a proof of Berthelot's conjecture on the preservation of overconvergent isocrystals by smooth proper pushforward.

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Cite

BibTeXRIS
BibTeX
@misc{qin2026arithmetic,
  title = {{The arithmetic de Rham stack}},
  author = {Junhui Qin},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.20203},
  eprint = {2608.20203},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.20203},
}
RIS
TY  - UNPB
TI  - The arithmetic de Rham stack
AU  - Junhui Qin
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.20203
UR  - https://arxiv.org/abs/2608.20203
AB  - We define and study the arithmetic de Rham stack X^arith of a scheme X over a field of characteristic p, and analyze its relation with related stacks such as the Hyodo--Kato stack. We show that X^arith gives a stack-theoretic approach to rigid cohomology and its coefficients, known as overconvergent isocrystals and arithmetic D-modules, which avoids the long-standing problem of frame-choosing in earlier approaches. We finally give some arithmetic applications of our formalism, such as a proof of Berthelot's conjecture on the preservation of overconvergent isocrystals by smooth proper pushforward.
ER  -