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    • CommentRowNumber1.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 21st 2022

    Started page.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 21st 2022
    • (edited Nov 21st 2022)

    Thanks for adding good stuff!

    On formatting:

    I have slightly adjusted the typesetting of the (co)limits by placing their indices below the arrow:

      $$
        A_{\square}[S]
        \;=\;
        \underset
          {\underset{ A'\subseteq A }{ \rightarrow }}
          {\lim}
        \;
        \underset
          {\underset{i}{\leftarrow}}
          {\lim}
        \;
        A'\big[S_{i}\big]
      $$
    

    By the way, just by enclosing technical terms in double square brackets, they get automatically hyperlinked to their respective entries, which is much of what the point of the wiki is about.

    This certainly works for basics like ring ([[ring]]), subring ([[subring]]), profinite integers ([[profinite integers]]) etc.

    For something like “condensed AA-modules” we can typeset as [[condensed module|condensed $A$-modules]] and then create an entry titled “condensed module”.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 21st 2022
    • (edited Nov 21st 2022)

    By the way, do you mean to write “derived \infty-category”, or is this rather just “\infty-category”?

    The question is whether you mean just the homotopy category. This matters later when the entry speaks about the map of hom-objects being an “isomorphism”. From looking (just) at Mann’s abstract, I suspect this is really meant to be an equivalence of hom-spaces (i.e. of hom-\infty-groupoids)?

    • CommentRowNumber4.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 21st 2022
    Thanks for the fixes! I think it should be "derived $\infty$-category" (i.e. complexes of modules) and not just $\infty$-category. This is discussed in page 15 of Mann's arxiv preprint. Mann further gives 1.3 of Lurie's Higher Algebra as reference.
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 21st 2022

    I see, thanks. So let’s say:

    … the (“derived”) \infty-category of chain complexes of

    with pointer to “(infinity,1)-category of chain complexes”.

    diff, v4, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 21st 2022

    and so I have expanded the “the canonical map … is an isomorphism” to:

    the canonical map of mapping objects … is an equivalence

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 22nd 2022

    Added a brief sentence on globalization and added a section for coherent duality, to be filled in later.

    diff, v6, current

    • CommentRowNumber8.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 22nd 2022

    Added the statement of Theorem 11.1 (Coherent Duality) from Scholze’s Lectures on Condensed Mathematics. The statement is currently verbatim, and I am planning to make edits in the future to give it more context.

    diff, v8, current

    • CommentRowNumber9.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 22nd 2022

    Added section on the six operations.

    diff, v8, current

    • CommentRowNumber10.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 24th 2022

    Started a section on Mann’s application of solid modules.

    diff, v10, current

    • CommentRowNumber11.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 24th 2022

    Added Zavyalov reference.

    diff, v10, current

    • CommentRowNumber12.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 25th 2022

    Starting to add a little more detail for the six-functor formalism for solid modules. Will fill in more later.

    diff, v11, current

    • CommentRowNumber13.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 25th 2022

    Added mention of Mann’s p-torsion Riemann-Hilbert correspondence.

    diff, v13, current

    • CommentRowNumber14.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 25th 2022

    Added statement of Poincare duality, included some pinpoint references, and corrected some typos. Might add statement of Mann’s p-torsion Riemann-Hilbert correspondence later, however this needs definitions of phi-modules and overconvergent etale sheaves.

    diff, v13, current