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PreprintCC BY-NC-SA 4.0arXiv

A note on prismatic sites for p-quasisyntomic rings

  • Jingbang Guo
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Abstract

Let p be a fixed prime number and let R be a p-quasisyntomic ring. We provide conditions for objects in the absolute prismatic site RPrism to cover the final object in Shv(RPrism) and to admit finite self-coproducts in RPrism. More precisely, we introduce in RPrism the so-called transversal objects, so that the coproduct of any object in RPrism with a transversal object exists in RPrism. As an immediate generalization, we introduce the so-called relatively quasiregular semiperfectoid covers of R, whose prismatic cohomology (of δ-pairs, in the sense of Antieau-Krause-Nikolaus) produces objects in RPrism that cover the final object in Shv(RPrism) and admit finite self-coproducts in RPrism.

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Cite

BibTeXRIS
BibTeX
@misc{guo2026note,
  title = {{A note on prismatic sites for p-quasisyntomic rings}},
  author = {Jingbang Guo},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2607.04931},
  eprint = {2607.04931},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.04931},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - A note on prismatic sites for p-quasisyntomic rings
AU  - Jingbang Guo
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2607.04931
UR  - https://arxiv.org/abs/2607.04931
AB  - Let p be a fixed prime number and let R be a p-quasisyntomic ring. We provide conditions for objects in the absolute prismatic site R_Prism to cover the final object in Shv(R_Prism) and to admit finite self-coproducts in R_Prism. More precisely, we introduce in R_Prism the so-called transversal objects, so that the coproduct of any object in R_Prism with a transversal object exists in R_Prism. As an immediate generalization, we introduce the so-called relatively quasiregular semiperfectoid covers of R, whose prismatic cohomology (of δ-pairs, in the sense of Antieau-Krause-Nikolaus) produces objects in R_Prism that cover the final object in Shv(R_Prism) and admit finite self-coproducts in R_Prism.
ER  -