Timeline for Connectedness, loops and formal moduli problems
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2021 at 10:13 | comment | added | Jon Pridham | The point is that $X(k)$ is the only connected space; the spaces $X(A)$ for Artinian rings are not, unless the DGLA in concentrated in non-positive cochain degrees. Contrast this with the notation $BG$ for the stack of $G$-torsors, whose stalks are connected in the sense that $(BG)(A)= B(G(A))$ for any Henselian ring $A$. | |
| Dec 13, 2021 at 0:18 | comment | added | A Rock and a Hard Place | @JonPridham: Agreed! But I don't quite see why this objection applies to the case at hand. (Pardon if I am missing something!) One of the requirements in the definition of a formal moduli problem is that $X(k)$, which may be thought of as the space of $k$-valued points of $X$, must be contractible. So $X$ has only a single "object", at least up homotopy (which is the best we can ask for anyway). On the other hand, Gaitsgory-Roseblyum also have a version of the correspondence between Lie algebroids and some kind of multi-object FMPs, where the objection to using $B$ might well be applicable. | |
| Dec 11, 2021 at 23:50 | comment | added | Jon Pridham | Reiterating a comment I made on the question, BG is not good notation for an infinitesimal functor with many objects (essentially the Deligne groupoid in this case). | |
| Aug 28, 2020 at 10:08 | history | edited | A Rock and a Hard Place | CC BY-SA 4.0 |
corrected typo
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| Apr 2, 2020 at 14:22 | history | edited | A Rock and a Hard Place | CC BY-SA 4.0 |
Added discussion of group objects in E_n-FMPs
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| Mar 3, 2020 at 2:33 | comment | added | Dmitry Vaintrob | Thanks! This is a funny property, that the delooping functor is an equivalence but the category is not stable. I wonder if there are other examples. And thanks for the correction: $E_n$ moduli problems are represented by $E_n$ algebras via a duality functor, so presumably a group object (in a geometric sense) would be representable by an $E_{n+1}$ algebra. | |
| Mar 3, 2020 at 2:31 | vote | accept | Dmitry Vaintrob | ||
| Mar 2, 2020 at 3:02 | history | edited | A Rock and a Hard Place | CC BY-SA 4.0 |
Unifying notation
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| Mar 2, 2020 at 2:52 | history | edited | A Rock and a Hard Place | CC BY-SA 4.0 |
deleted 1 character in body
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| Mar 1, 2020 at 20:40 | history | edited | A Rock and a Hard Place | CC BY-SA 4.0 |
Adding a little more details
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| Mar 1, 2020 at 6:22 | history | edited | A Rock and a Hard Place | CC BY-SA 4.0 |
Adding a little more details
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| Mar 1, 2020 at 5:55 | history | edited | A Rock and a Hard Place | CC BY-SA 4.0 |
Adding a little more details
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| Mar 1, 2020 at 5:40 | history | answered | A Rock and a Hard Place | CC BY-SA 4.0 |