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May 24, 2021 at 18:36 comment added Watson Your answer is not correct (please see Prof. Zarhin's comment below).
May 23, 2021 at 16:29 vote accept Watson
May 24, 2021 at 16:10
May 23, 2021 at 13:43 comment added Will Sawin If they're not geometrically simple, the endomorphism algebra splits as a product of matrix algebras over division algebras, and applying your argument to those division algebras seems to do the trick.
May 23, 2021 at 13:34 history answered user166831 CC BY-SA 4.0