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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.
4
votes
Accepted
Global centralizers in Jordan-Chevalley decomposition in bad characteristic
The answer is affirmative for $G$ any smooth affine $k$-group. We may assume $p = {\rm{char}}(k) > 0$. By 14.26 in Borel's textbook on algebraic groups, $n$ is in the Lie algebra of a unipotent subgro …
10
votes
Are linear algebraic groups rigid?
A most excellent example of "non-rigidity" beyond the reductive case (depending on how loose one wants to be about the meaning of "rigidity")
is given in 5.2--5.10 of Exp. XIX of SGA3: a smooth affin …