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Results tagged with algebraic-groups
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user 56878
Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.
2
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1
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Why is the set of parabolic reductions of a G-torsor E bijective to the set of parabolic sub...
Let $G$ be a reductive group scheme over some base $X$ and $P \subseteq G$ a parabolic subgroup. To a $P$-torsor $\mathscr{E}_P$, we may associate a $G$-torsor $\mathscr{E} = G \times^P \mathscr{E}_P$ …
- 3,058
2
votes
Accepted
Why is the set of parabolic reductions of a G-torsor E bijective to the set of parabolic sub...
Thanks to Laurent Moret-Bailly for pointing out that I missed a crucial hypothesis! Now I can construct the quasi-inverse, which I'll record below in case some future person is confused by the same pr …
- 3,058