Dieudonné theory via cohomology of classifying stacks

Mondal, Shubhodip

doi:10.1017/fms.2021.77

Cited by 2 publications

(1 citation statement)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us consider the reduction modulo of the spectral sequence (⚃), which computes the crystalline cohomology of by the crystalline comparison. Using the fact that (see, for instance, [Mon21, Theorem 1.2]), we see that modulo must be zero.…”

Section: An Examplementioning

confidence: 99%

On the u^∞-torsion submodule of prismatic cohomology

Li¹,

Liu²

2023

Compositio Math.

View full text Add to dashboard Cite

We investigate the maximal finite length submodule of the Breuil–Kisin prismatic cohomology of a smooth proper formal scheme over a $p$ -adic ring of integers. This submodule governs pathology phenomena in integral $p$ -adic cohomology theories. Geometric applications include a control, in low degrees and mild ramifications, of (1) the discrepancy between two naturally associated Albanese varieties in characteristic $p$ , and (2) the kernel of the specialization map in $p$ -adic étale cohomology. As an arithmetic application, we study the boundary case of the theory due to Fontaine and Laffaille, Fontaine and Messing, and Kato. Also included is an interesting example, generalized from a construction in Bhatt, Morrow and Scholze's work, which illustrates some of our theoretical results being sharp, and negates a question of Breuil.

show abstract

Section: An Examplementioning

confidence: 99%

On the u^∞-torsion submodule of prismatic cohomology

Li¹,

Liu²

2023

Compositio Math.

View full text Add to dashboard Cite

show abstract

𝑝-Adic Hodge Theory for Artin Stacks

Kubrak,

Prikhodko

2024

Memoirs of the AMS

View full text Add to dashboard Cite

This work is devoted to the study of integral p p -adic Hodge theory in the context of Artin stacks. For a Hodge-proper stack, using the formalism of prismatic cohomology, we establish a version of p p -adic Hodge theory with the étale cohomology of the Raynaud generic fiber as an input. In particular, we show that the corresponding Galois representation is crystalline and that the associated Breuil-Kisin module is given by the prismatic cohomology. An interesting new feature of the stacky setting is that the natural map between étale cohomology of the algebraic and the Raynaud generic fibers is often an equivalence even outside of the proper case. In particular, we show that this holds for global quotients [ X / G ] [X/G] where X X is a smooth proper scheme and G G is a reductive group. As applications we deduce Totaro’s conjectural inequality and also set up a theory of A i n f A_{\mathrm {inf}} -characteristic classes.

show abstract

Dieudonné theory via cohomology of classifying stacks

Cited by 2 publications

References 31 publications

On the u^∞-torsion submodule of prismatic cohomology

On the u^∞-torsion submodule of prismatic cohomology

𝑝-Adic Hodge Theory for Artin Stacks

Contact Info

Product

Resources

About

Dieudonné theory via cohomology of classifying stacks

Cited by 2 publications

References 31 publications

On the u∞-torsion submodule of prismatic cohomology

On the u∞-torsion submodule of prismatic cohomology

𝑝-Adic Hodge Theory for Artin Stacks

Contact Info

Product

Resources

About

On the u^∞-torsion submodule of prismatic cohomology

On the u^∞-torsion submodule of prismatic cohomology