Pith. sign in

REVIEW 11 cited by

The prismatization of $p$-adic formal schemes

Not yet reviewed by Pith; the record is open.

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 2201.06124 v1 pith:ZWOEPPDM submitted 2022-01-16 math.AG math.NT

classification math.AGmath.NT
keywords adicformalmathrmwcartattachedcartier--wittcohomologycrystals
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

In this note, we introduce and study the Cartier--Witt stack $\mathrm{WCart}_X$ attached to a $p$-adic formal scheme $X$ as well as some variants. In particular, we reinterpret the notion of prismatic crystals on $X$ and their cohomology in terms of quasicoherent sheaf theory on $\mathrm{WCart}_X$ in favorable situations.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 11 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. Higher dimensional dominoes in de Rham-Witt cohomology

    math.AG 2026-07 accept novelty 7.0 of 10

    Two-dimensional dominoes in de Rham–Witt cohomology are classified by orbits of Frobenius-skew polynomials, all dominoes admit a triangular normal form, and the resulting theory bounds the p-primary Brauer exponent of...

  3. Algebraization of absolute perfectoidization via section rings

    math.AG 2026-04 unverdicted novelty 7.0 of 10

    Graded absolute perfectoidization of G-graded adic rings yields an algebraization of the structure sheaf of projective-type formal schemes.

  4. The Shimurian BT stack is a gerbe over truncated displays

    math.AG 2025-10 accept novelty 7.0 of 10

    The mod p Shimurian BT stack is a gerbe over the stack of truncated displays, confirming Drinfeld's gerbe conjecture.

  5. 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...

  6. An obstruction to lifting schemes to spectral schemes

    math.AG 2026-07 accept novelty 6.5 of 10

    A scheme over Z lifts to a spectral scheme over S only if it carries a compatible ˆδ-structure; this obstruction is functorial and kills lifts of rings of integers, Ga, GLn and many closed subschemes of Pn.

  7. Tannakian reconstruction in derived algebraic geometry

    math.AG 2026-08 conditional novelty 6.0 of 10

    Derived analogues of the Tannakian reconstruction theorems of Lurie and Bhatt-Halpern-Leistner are proved over animated rings, with QCoh enhanced to a Θ-category carrying the symmetric algebra monad.

  8. Ring stacks conjecturally related to the stacks $BT_n^{G,\mu}$

    math.AG 2025-10 conditional novelty 6.0 of 10

    This paper defines the ring stacks sRn and sR⊕n from the ring space of sheared Witt vectors and builds several explicit quasi-isomorphic models for them.

  9. 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.

  10. De Rham-Higgs comparison for mixed Hodge modules in positive characteristic

    math.AG 2025-07 conditional novelty 6.0 of 10

    A de Rham-Higgs comparison for mixed-Hodge-module-inspired subcomplexes is established in special positive-characteristic cases, yielding decomposition and vanishing theorems when the logarithmic cotangent bundle spli...

  11. 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.

Pith tools