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Generalised representations as q-connections in integral $p$-adic Hodge theory
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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.
Forward citations
Cited by 2 Pith papers
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Prismatic cohomology and $A_{\inf}$-cohomology with coefficients
Prismatic cohomology of a locally finite free prismatic crystal is canonically isomorphic to A_inf-cohomology of the associated relative Breuil-Kisin-Fargues module, for smooth p-adic formal schemes over the ring of i...
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A prismatic-etale comparison theorem in the semistable case
Breuil-Kisin cohomology of analytic log prismatic F-crystals on semistable p-adic formal schemes is canonically isomorphic, after tensoring with A_inf and inverting mu, to the etale cohomology of the corresponding sem...
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