Timeline for Heuristics for 2-morphisms of (algebraic) stacks
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2015 at 2:48 | comment | added | S. Carnahan♦ | If $f$ and $g$ are given by $H$-equivariant maps $\tilde{f}, \tilde{g}: P \to V$, where $P$ is an $H$-torsor over $[U/G]$, then a 2-morphism $f \Rightarrow g$ is a section of $H$ on $V$ whose action takes $\tilde{f}$ to $\tilde{g}$. | |
| Feb 7, 2015 at 19:28 | comment | added | Qfwfq | I see. But.. it sounds somehow.. artificial (though correct, of course). What's an automorphism of a family of elliptic curves over $X$ in terms of the geometry of $X$? Perhaps the (more local) question I want to ask is: what's a 2-morphism between $f,g:[U/G]\to [V/H]$ in terms of the geometry of the two actions? (But this I can think by myself I guess) | |
| Feb 7, 2015 at 3:18 | comment | added | S. Carnahan♦ | @Qfwfq Nothing really changes. A 1-morphism $X \to Y$ produces a family of elliptic curves over the stack $X$, and a 2-morphism is an automorphism of the family. This is why I didn't bother to make $X$ complicated. | |
| Feb 5, 2015 at 11:02 | comment | added | Qfwfq | And if $X$ is any scheme, you get the family version of your example, as for any other moduli stack. But, what if $X$ itself is a (non rigid) stack? | |
| Feb 5, 2015 at 10:15 | history | answered | S. Carnahan♦ | CC BY-SA 3.0 |