Generalised representations as q-connections in integral $p$-adic Hodge theory

Matthew Morrow; Takeshi Tsuji

Generalised representations as q-connections in integral $p$-adic Hodge theory

Number Theory 2021-07-02 v2 Algebraic Geometry

Authors: Matthew Morrow , Takeshi Tsuji

Abstract

We relate various approaches to coefficient systems in relative integral $p$ -adic Hodge theory, working in the geometric context over the ring of integers of a perfectoid field. These include small generalised representations over $A_{\text{inf}}$ inspired by Faltings, modules with q-connection in the sense of q-de Rham cohomology, crystals on the prismatic site of Bhatt--Scholze, and q-deformations of Higgs bundles.

Keywords

p-adic Hodge theory q-connection prismatic site generalised representations perfectoid field Higgs bundles

Cite

@article{arxiv.2010.04059,
  title  = {Generalised representations as q-connections in integral $p$-adic Hodge theory},
  author = {Matthew Morrow and Takeshi Tsuji},
  journal= {arXiv preprint arXiv:2010.04059},
  year   = {2021}
}

Comments

Version 2 with new material: global comparison between prismatic F-crystals and relative Breuil--Kisin--Fargues modules, and details of the Dieudonn\'e theory. Also minor changes and corrections

Generalised representations as q-connections in integral $p$-adic Hodge theory

Abstract

Keywords

Cite

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