BIRS Workshop Lecture Videos
Rigidity for Unirational Groups Rosengarten, Zev
One of the most fundamental results underlying the theory of abelian varieties is "rigidity" -- that is, that any k-scheme morphism of abelian varieties which preserves identities is actually a k-group homomorphism. This result depends crucially upon the properness of such varieties. For affine groups in general, there is no analogous rigidity statement. We will nevertheless show that such a rigidity result holds for unirational groups (which are always affine) satisfying certain conditions, and discuss several implications.
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