Timeline for Phenomena of gerbes
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 26, 2017 at 2:07 | comment | added | Dan Petersen | Yes, it's always faithful. But you're right: you need to invert the primes 2 and 3 to get the isomorphism $\overline M_{1,1} \cong \mathbb P(4,6)$. | |
| Mar 25, 2017 at 22:34 | comment | added | André Henriques | @Dan. Yes, over $\mathbb C$, that's a description of those stacks. But my statement also holds over $\mathbb Q$. Over rings of positive characteristic (e.g. characteristic two), I'm not sure whether the action of $\mathbb Z/2$ on an elliptic curve is always faithful. Is it always faithful? | |
| Mar 25, 2017 at 21:15 | comment | added | Dan Petersen | If you consider the Deligne-Mumford compactifications instead, then the statement is that the orbifold projective line $\mathbb P(4,6)$ is a $\mathbb Z/2$-gerbe over the orbifold projective line $\mathbb P(2,3)$. | |
| Mar 7, 2017 at 20:40 | comment | added | Will Sawin | I believe this other moduli stack is the moduli stack of genus 0 modular curves with 4 marked points, one unlabeld and three labeled. | |
| Mar 7, 2017 at 14:55 | comment | added | Ariyan Javanpeykar | Uninteresting remark: The DM stack is (by definition) "the rigidification of the moduli stack of elliptic curves with respect to the flat normal subgroup $\{\pm 1\}$ of the inertia stack". That's a nice name right? | |
| Mar 6, 2017 at 23:28 | history | edited | André Henriques | CC BY-SA 3.0 |
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| Mar 6, 2017 at 22:53 | history | answered | André Henriques | CC BY-SA 3.0 |