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A reductive group is an algebraic group $G$ over an algebraically closed field such that the unipotent radical of $G$ is trivial

1 vote

degeneration of reductive group

SGA3 XIX section 5 has a terrifying example of $PGL(2)$ degenerating into something solvable. Thanks to grghxy.
3 votes
2 answers
355 views

degeneration of reductive group

If $A$ is a mixed characteristic complete DVR (I'm only actually interested in $\mathbf{Z}_p$) and $G/A$ is a closed subgroup scheme of $GL(n)$ whose generic fibre is connected reductive and split, is …
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3 votes
2 answers
450 views

Representations of complex semi-simple algebraic group "defined over $\mathbf{Z}$"?

If $G$ is a split semisimple linear algebraic group over $\mathrm{Spec}(\mathbf{Z})$ then does every (algebraic) irrep of $G_{\mathbf{C}}$ extend to a morphism $G\to\mathrm{GL}_n$ over $\mathrm{Spec}( …
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