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Feb
1
awarded  Popular Question
Jan
31
awarded  Popular Question
Jan
31
comment Intuition for the Cartan connection and “rolling without slipping” in Cartan geometry
@RobertBryant: thanks for your comment. Is there a reference for this kind of things? (maybe the book by R.W.Sharpe "Cartan's generalization of [...]"?)
Jan
29
comment Intuition for the Cartan connection and “rolling without slipping” in Cartan geometry
Great answer. "There can be, and, often, there is, more information [...]": could you also sketch which further information is always contained in that piece of data?
Jan
29
revised Intuition for the Cartan connection and “rolling without slipping” in Cartan geometry
edited body
Jan
28
comment What is the mathematical significance of the IHES logo?
Oh I've always thought it was some sort of (unreadable) monogram of the letters "IHES", I'm delighted it has some actual mathematical meaning :)
Jan
26
revised Fiberwise criterion for a stack to be a gerbe
added 50 characters in body
Jan
26
comment Fiberwise criterion for a stack to be a gerbe
@Ariyan. Thanks a lot for your comments!
Jan
26
comment Fiberwise criterion for a stack to be a gerbe
@Ariyan: yes, of course, all $G$-torsors over $\mathrm{Spec}\,\mathbb{C}$ are trivial. I think I really wanted to ask this instead: working in the category of $\mathbb{C}$-schemes, if $S$ is a scheme and $G$ and $H$ non isomorphic group schemes over $S$, can it happen that $BG\cong BH$ (as stacks over $S$)? (here $BG:=[*/G/S]$ as per L.MB.'s book)
Jan
26
comment Fiberwise criterion for a stack to be a gerbe
@Ariyan: interesting - can it even happen over $\mathbb{C}$? I mean, that $BG\cong BH$ for non isomorphic complex algebraic groups $G$ and $H$.
Jan
26
awarded  Nice Question
Jan
25
comment Polynomials with the same values set on the unit circle
Oops, sure. Deleted my comment.
Jan
25
comment Fiberwise criterion for a stack to be a gerbe
But the group schemes $\mu_3$ and $\mathbb{Z}/3$ themselves are not isomorphic over $\mathbb{Q}$, right? On the $\mathbb{Q}$-algebra $\mathbb{Q}$, the first has value the trivial group (1 is the only third root of unity in $\mathbb{Q}$), while the second has value $\mathbb{Z}/3$. Can taking $B(.)$ make them into isomorphic gerbes already over $\mathbb{Q}$?
Jan
25
revised Fiberwise criterion for a stack to be a gerbe
added 155 characters in body
Jan
25
revised Fiberwise criterion for a stack to be a gerbe
added 700 characters in body
Jan
25
comment Fiberwise criterion for a stack to be a gerbe
Fibres are $BG$. It doesn't seem flat to me though. If $*:=\mathrm{Spec}(\mathbb{C})$, then $*\to BG$ is an étale atlas, in particular smooth hence flat; so if $f$ were flat it would be at every point of source, and the the composition $*\to BG\to\mathbb{A}^1$ would be flat but it's not. Does it work?
Jan
25
answered Fiberwise criterion for a stack to be a gerbe
Jan
20
comment Understanding the Exp map from a moduli of smooth curves
What's a "curve" in this context? And how is their "moduli space" defined?
Jan
16
revised An example for affine function
edited body
Jan
7
accepted Definition of étale (etc) for non-representable morphisms of algebraic stacks?