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edited Aug 1, 2012 at 14:56

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Is everyany simple abelian variety covered by a non-simple abelian variety

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asked Aug 1, 2012 at 13:39

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Is every simple abelian variety covered by a non-simple abelian variety

Let $A/k$ be a simple abelian variety.

Does there exist a non-simple abelian variety $B/k$ and a finite homomorphism $f:B\to A$ over $k$?

I don't need $f:B\to A$ to be etale.

abelian-varieties arithmetic-geometry ag.algebraic-geometry