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Apr 25, 2010 at 0:41 comment added BCnrd Automorphism schemes of projective varieties intervene in the method (prior to intervention of abelian varieties!), so unless one knows results on finite generation of their component groups (an open problem in most cases) there's no way one can make such an algorithm. Over global function fields the relatively new theory of pseudo-reductive groups has brought us to the same degree of progress as the number field case. As best I can tell, finiteness properties of component groups of Aut-schemes are intractable in general.
Oct 29, 2009 at 7:58 vote accept Jonah Sinick
Oct 29, 2009 at 7:26 answer added Pete L. Clark timeline score: 4
Oct 29, 2009 at 6:54 history asked Jonah Sinick CC BY-SA 2.5