Ogus's conjecture is resolved affirmatively in full generality by constructing the required F-isocrystal via p-adic local systems and prismatic methods, while also introducing a prismatic refinement of the p-adic Riemann-Hilbert functor.
Crystalline representations and Wach modules in the relative case II
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study relative Wach modules generalising our previous works on this subject. Our main result shows a categorical equivalence between relative Wach modules and lattices inside relative crystalline representations. Using this result, we deduce a purity statement for relative crystalline representations and provide a criteria for checking crystallinity of relative $p$-adic representations. Furthermore, we interpret relative Wach modules as modules with $q$-connections, and show that for a crystalline representation, its associated Wach module together with the Nygaard filtration is the canonical $q$-deformation (after inverting $p$) of the filtered $(\varphi,\partial)$-module associated to the representation.
verdicts
UNVERDICTED 2representative citing papers
Proves natural equivalence between analytic prismatic F-crystals on the absolute prismatic site and relative Wach modules via correspondence of Galois action with prismatic stratification, plus new descent results.
citing papers explorer
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Ogus's conjecture on F-isocrystals
Ogus's conjecture is resolved affirmatively in full generality by constructing the required F-isocrystal via p-adic local systems and prismatic methods, while also introducing a prismatic refinement of the p-adic Riemann-Hilbert functor.
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Prismatic $F$-crystals and Wach modules
Proves natural equivalence between analytic prismatic F-crystals on the absolute prismatic site and relative Wach modules via correspondence of Galois action with prismatic stratification, plus new descent results.