Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 28th 2010

    All three of these entries (algebraic stack, Deligne-Mumford stack and Artin stack ) need careful polishing and expansion. My suggestion is that we eventually expand algebraic stack to a comprehensive discussion and have the other two be more or less clarification of terminology and otherwise be just redirects.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeDec 29th 2010

    I should repeat again that what Lurie calls Deligne-Mumford is according to him not quite the same in details to what others call Deligne-Mumford. The entry seems to be mixing theorems/characterizations on both variants as if there were the same.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2010

    Lurie does not require separatedness.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeDec 29th 2010
    • (edited Dec 29th 2010)

    Aha. Is this spoiling the local picture of a scheme modulo finite group (with condition on slices) quotient interpretation or not ?

    P.S. people talk also of Deligne-Mumford orbifolds in differentiable settings.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2010

    I was planning today to sit down and nn-labify the nice chapter on algebraic stacks in The Stacks Project document to clearly expose the relation between the various axioms and the notion of groupoids internal to algebraic spaces. But it seems that I won’t find the time soon.

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeDec 29th 2010
    • (edited Dec 29th 2010)

    This nice idea may be a little tricky as it may contaminate nnLab with various copy licences which are pretty detailed in their case.

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeDec 29th 2010
    • (edited Dec 29th 2010)

    In a differentiable setup

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2010

    This nice idea may be a little tricky as it will contaminate nLab with various copy licences which are pretty detailed in their case.

    Well, I read material all the time in books and papers and then write out my understanding of it on the nnLab. We don’t need to (and probably don’t even want to) copy material verbatim.

    • CommentRowNumber9.
    • CommentAuthorzskoda
    • CommentTimeDec 29th 2010
    • (edited Dec 29th 2010)

    Good. I misunderstood the phrase :)

    • CommentRowNumber10.
    • CommentAuthorzskoda
    • CommentTimeDec 29th 2010

    Robbin-Salamon is very good as it emphasises the relations between groupoid point of view and atlases and few other points of relation between concrete and abstract nonsense. Also becuase it does it in differentiable setup.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2023

    added pointer to the original:

    diff, v6, current