Pith. sign in

REVIEW 10 cited by

Absolute prismatic cohomology

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2201.06120 v1 pith:42GBXACY submitted 2022-01-16 math.AG math.NT

Bhargav Bhatt , Jacob Lurie This is my paper · ORCID
classification math.AGmath.NT
keywords prismaticabsolutecohomologyadiccallcartier-wittcrystalformal
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

The goal of this paper is to study the absolute prismatic cohomology of $p$-adic formal schemes. We do so by recasting the notion of a prismatic crystal on $\mathrm{Spf}(\mathbf{Z}_p)$ in terms of quasicoherent sheaves on a geometric object we call the Cartier-Witt stack.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Reduction modulo p of crystalline Galois representations via {\mu}_p-equivariance

    math.NT 2026-07 accept novelty 8.0 of 10

    Crystalline Galois representations acquire mu_p-equivariant Breuil-Kisin module reductions, yielding the ↑ constraint on inertial weights and proving weight elimination for a general Serre weight conjecture.

  2. Sheared displays and $p$-divisible groups

    math.NT 2026-01 conditional novelty 8.0 of 10

    Over p-nilpotent rings, p-divisible groups are equivalent to sheared displays, resolving Drinfeld's conjecture and giving a Dieudonné theory for all p-divisible groups.

  3. $\mathbb{A}^1$-invariant motivic cohomology of schemes

    math.KT 2025-08 conditional novelty 8.0 of 10

    A new A1-invariant motivic cohomology for all qcqs schemes is constructed from the slice filtration of KGL, with a spectral sequence to homotopy K-theory and etale/syntomic comparisons.

  4. Perfect $F$-gauges and finite flat group schemes

    math.NT 2025-09 conditional novelty 7.0 of 10

    Over arbitrary p-adic formal bases, finite locally free p-power torsion commutative group schemes are exactly the perfect F-gauges of Tor amplitude [-1,0] and Hodge-Tate weights 0,1, via an exact, Cartier-duality-comp...

  5. Weibel vanishing and the projective bundle formula for mixed characteristic motivic cohomology

    math.AG 2025-07 conditional novelty 7.0 of 10

    Mixed characteristic motivic cohomology satisfies Weibel vanishing, the projective bundle formula, comparison to Milnor K-theory, and pro cdh descent.

  6. Beilinson--Lichtenbaum phenomenon for motivic cohomology

    math.AG 2025-06 conditional novelty 7.0 of 10

    Over Prüfer and valuation rings, p-adic motivic cohomology is the Nisnevich-local truncation of Bhatt-Lurie syntomic cohomology, and over Dedekind domains it recovers Bloch's cycle complexes.

  7. An integral comparison of crystalline and de Rham cohomology

    math.NT 2025-07 conditional novelty 6.0 of 10

    The paper proves an integral, coefficient-version of the Berthelot-Ogus comparison between de Rham and crystalline cohomology using stacky prismatic cohomology and a Dwork-trick argument.

  8. Moduli of truncated shtukas and displays

    math.AG 2025-06 conditional novelty 6.0 of 10

    Truncated shtukas and displays are classified by quotient stacks of loop groups by display groups, with explicit cutoff bounds N0 = 2C+1 beyond which truncation determines the full object.

  9. A note on prismatic sites for p-quasisyntomic rings

    math.AG 2026-07 accept novelty 5.0 of 10

    Transversal objects and relatively quasiregular semiperfectoid covers of a p-quasisyntomic ring R produce objects in R_Δ that cover the final object and admit finite self-coproducts.

  10. Some applications of the Nygaard filtration and quasisyntomic descent in positive characteristic

    math.AG 2025-07 accept novelty 4.0 of 10

    A mostly expository article that re-proves known p-adic comparison theorems with elementary tools and adds a new corollary about multiplication by n on fppf cohomology of abelian varieties.

Pith tools