Integral p-adic Hodge theory

Abstract

We construct a new cohomology theory for proper smooth (formal) schemes over the ring of integers of C_p. It takes values in a mixed-characteristic analogue of Dieudonne modules, which was previously defined by Fargues as a version of Breuil-Kisin modules. Notably, this cohomology theory specializes to all other known p-adic cohomology theories, such as crystalline, de Rham and etale cohomology, which allows us to prove strong integral comparison theorems. The construction of the cohomology theory relies on Faltings's almost purity theorem, along with a certain functor $L\eta$ on the derived category, defined previously by Berthelot-Ogus. On affine pieces, our cohomology theory admits a relation to the theory of de Rham-Witt complexes of Langer-Zink, and can be computed as a q-deformation of de Rham cohomology.

124 pages, v3: minor updates, final version

Cited by in corpus (19)

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• $K$-theory of valuation rings
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• Notes on the A_inf-cohomology of Integral p-adic Hodge theory
• CM liftings of K3 surfaces over finite fields and their applications to the Tate conjecture
• $p$-adic vanishing cycles as Frobenius-fixed points
• Periods of Drinfeld modules and local shtukas with complex multiplication
• Extended plus closure in complete local rings
• On commutative nonarchimedean Banach fields
• Some ring-theoretic properties of A_inf
• Complex orientations for THH of some perfectoid fields
• Categorical Logarithmic Hodge Theory, I
• The reduction of $G$-ordinary crystalline representations with $G$-structure
• On the p-typical de Rham-Witt complex over W(k)
• Height functions for motives, II
• On the existence of analytic families of G-stable lattices and their reductions
• Galois representations and ordinary reduction