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nLab > Latest Changes: prismatic cohomology

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1 to 38 of 38

  1.  
    • CommentRowNumber1.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 22nd 2019

    Stub to record today’s reference

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 22nd 2019

    The notion of δ\delta-rings was introduced by Joyal [Joy85] and studied extensively by Buium [Bui97] under the name of “pp-derivations”; see also [Bor16]

    I wonder if any light is cast on our discussions on arithmetic differential cohesion, e.g., from here, as appears at Borger’s absolute geometry.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 8th 2020

    Added a couple of places giving very brief insights, and removed the link to the other form of prism.

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJan 9th 2020
    δ-ring also links to a wrong entry.
    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 9th 2020

    I’ve removed that link for now. We have arithmetic differential geometry but don’t define a δ\delta-ring.

    diff, v5, current

    • CommentRowNumber6.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 1st 2022

    Added definitions of prismatic site and prismatic cohomology.

    diff, v6, current

    • CommentRowNumber7.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 1st 2022

    Typographical correction.

    diff, v6, current

    • CommentRowNumber8.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 1st 2022

    Typographical corrections.

    diff, v6, current

    • CommentRowNumber9.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 1st 2022

    Emphasis added for definitions.

    diff, v6, current

    • CommentRowNumber10.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 1st 2022

    Adding comparison theorems section.

    diff, v6, current

    • CommentRowNumber11.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 1st 2022

    Adding crystalline comparison theorem (planning to flesh these out more later).

    diff, v6, current

    • CommentRowNumber12.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 1st 2022

    Put comparison theorems in theorem environments.

    diff, v6, current

    • CommentRowNumber13.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 1st 2022

    Centered equations, added link to p-adic Hodge theory, and added reference to Bhatt-Lurie.

    diff, v7, current

    • CommentRowNumber14.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 1st 2022

    Rewrote comparison theorems. Added references to Drinfeld and Bhatt-Lurie’s other paper.

    diff, v7, current

    • CommentRowNumber15.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 1st 2022

    Typographical corrections.

    diff, v7, current

    • CommentRowNumber16.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added applications section.

    diff, v8, current

    • CommentRowNumber17.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Corrected typo.

    diff, v8, current

    • CommentRowNumber18.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Corrected typo.

    diff, v8, current

    • CommentRowNumber19.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Corrected odd typesetting of “IB”.

    diff, v8, current

    • CommentRowNumber20.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added links to the nlab pages for Bhargav Bhatt and Jacob Lurie.

    diff, v8, current

    • CommentRowNumber21.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 2nd 2022

    Hi Anton,

    thanks for all these edits! If you are adding substantial content in a sequences of edits, then it’s not necessary to add an edit comment when you fix a typo. And indeed, if you do a series of edits, you can make a comment on the first one, then on subsequent edits in the same session come over here to the nForum and edit the comment here to add in extra details about what you did, if you like.

    • CommentRowNumber22.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022
    Got it, thanks!
    • CommentRowNumber23.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added section on historical precursors (A_inf cohomology and THH).

    diff, v9, current

    • CommentRowNumber24.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 2nd 2022

    Added some more references (Kedlaya and Emerton’s notes, Chao Li’s notes from Bhatt’s lectures).

    diff, v9, current

  25. add ref

    anonymous

    diff, v10, current

    • CommentRowNumber26.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 20th 2022

    Added relation to p-adic etale K-theory and a reference to Bhatt’s ICM survey.

    diff, v12, current

    • CommentRowNumber27.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 20th 2022

    Separated the section for the definition of prism and created a new section for examples of prisms.

    diff, v13, current

    • CommentRowNumber28.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 20th 2022

    Starting a new section on the absolute prismatic cohomology, and will write up more on the stacky approach later.

    diff, v14, current

    • CommentRowNumber29.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 21st 2022

    Added section on prismatic crystals and mention of recent work by Drinfeld and Bhatt-Lurie on a stacky approach to prismatic crystals. Might expand more on this later.

    diff, v16, current

    • CommentRowNumber30.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 22nd 2022

    Added relation to perfectoid rings.

    diff, v18, current

    • CommentRowNumber31.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 22nd 2022

    Reworked stacky approach to prismatic crystals and added a pinpoint reference to Bhatt’s survey.

    diff, v19, current

    • CommentRowNumber32.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 29th 2022

    Changed link from “Hochschild homology” to “topological Hochschild homology” and added it to related concepts.

    diff, v20, current

    • CommentRowNumber33.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 30th 2022

    Added reference to work of Antieau, Krause, and Nikolaus applying prismatic cohomology to algebraic K-theory.

    diff, v21, current

    • CommentRowNumber34.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 30th 2022

    Added a mention of the Nygaard filtration.

    diff, v21, current

    • CommentRowNumber35.
    • CommentAuthorUrs
    • CommentTimeNov 30th 2022

    enclosing author name in double square brackets, to hyperlink them to their pages:

    diff, v22, current

    • CommentRowNumber36.
    • CommentAuthorAnton Hilado
    • CommentTimeDec 1st 2022

    Mentioning that prismatic cohomology is a cohomology theory for p-adic formal schemes.

    diff, v24, current

    • CommentRowNumber37.
    • CommentAuthorAnton Hilado
    • CommentTimeJul 23rd 2023

    Creating new page on prismatization and linking to it.

    diff, v25, current

    • CommentRowNumber38.
    • CommentAuthorJohn Baez
    • CommentTimeOct 4th 2024

    Added link to page Joyal delta-ring, and a really quick comment on what they’re used for.

    diff, v27, current

1 to 38 of 38

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