Timeline for What does the moduli stack of G-torsors over the multiplicative group look like?
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| Aug 6, 2013 at 11:43 | comment | added | Jason Starr | @Chris: It is not the opposite. The same argument as in the exercise applies to any (tame) multiplicative group $T$. For every smooth, connected, linear algebraic group $G$ (over a field in that exercise, but the same argument works relatively), every $T$-torsor over $G$ is induced from a unique extension of group schemes of $G$ by $T$. Now take $G$ to be $\mathbb{G}_m$ and take $T$ to be a finite Abelian group of order prime to $p$. | |
| Aug 6, 2013 at 9:13 | comment | added | Chris Schommer-Pries | I looked up exercise 7.1 in Dolgachev's "Lectures on Invariant Theory". It has to do with $\mathbb{G}_m$ bundles over a connected algebraic group G. This is opposite to what I was asking. I want G-bundles not $\mathbb{G}_m$-bundles. Moreover in my case G is a finite group, so not connected. | |
| Aug 6, 2013 at 1:22 | history | edited | Jason Starr | CC BY-SA 3.0 |
Added tame hypothesis -- still considering the wild case.
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| S Aug 6, 2013 at 1:09 | history | answered | Jason Starr | CC BY-SA 3.0 | |
| S Aug 6, 2013 at 1:09 | history | made wiki | Post Made Community Wiki by Jason Starr |