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nLab > Latest Changes: A Survey of Eilliptic Cohomology - the derived moduli stack of derived elliptic curves

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 3rd 2009
    • (edited Nov 3rd 2009)
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 3rd 2009
    HELP:

    I need the following for connecting the two main sections at this entry. I thought I knew this, but now I am feeling a bit uncertain:

    what is, if any, the explicit expression for the respresenting (oo,1)-topos of a G-scheme that is given as a sheaf on G?

    In particular for the case of derived Deligne-Mumford stacks, in theorem 2.6.16 of Structured Spaces:

    the theorem states that given F it is representable by (X,O_X).

    How do I express X in terms of F here?

    It should be this, but I am a bit worried:

    X should be the oo,1-topos of oo-stacks on the site G/F.

    Is it?
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 3rd 2009
    Hm, I think I get it. The DM stack as a groupoid appears essentially as the object U in the second paragraph below the diagram on p. 80 of Structured Spaces and Y/U is the topos of sheaves "on the groupoid".
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 4th 2009
    polished introduction and beginning of the first part
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 4th 2009
    I worked the morrning over on the entry A Survey of Elliptic Cohomology - the derived moduli stack of derived elliptic curves,

    on the subsection "notions of space".

    This is now effectively (in as far as it achieves what it means to achieve) a srvey of the key ideas in Structured Spaces . I am thinking of copying that subsection eventually to this entry.

    This should be of interest to anyone who took interest in the discussion on comparative smootheology.
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 6th 2013

    copied some of the paragraphs to moduli stack of elliptic curves and polished slightly.

    An improvement over the previous sad situation, but still not good.

1 to 6 of 6

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