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Results tagged with algebraic-groups
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user 39304
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.
9
votes
Accepted
Exactness of the Weil restriction functor $\mathrm{Res}_{X/k}$
It is not right exact. Assume that $k$ is algebraically closed. If the map $Res_{X/k}B\to Res_{X/k}C$ was surjective as a map of sheaves for the fppf topology, then in particular, the map on sections …
- 7,377
9
votes
Accepted
Example of a connected finite group scheme which is not solvable
The connected finite kernel $H$ is not solvable, provided that $n>2$ or $p>2$, see the edit below.
$\def\eps{\varepsilon} \def\m{\mathfrak{m}}$Suppose by contradiction that $H$ is solvable and the $m$ …
- 12.9k
6
votes
Accepted
Cohomological interpretation of G-equivariant line bundles
See Theorem 4.2.2 in https://www-fourier.ujf-grenoble.fr/~mbrion/lin.pdf
In particular, in your example properness of $X=G/B$ simplifies the left part of the sequence, turning it into $$0\to \hat{G} …
- 7,377