# The Picard group ao abelian varieties

Dear, my question is: If A and B are abelian varieties over an algebraically closed field, then Pic ^ {0} (A x B) = Pic ^ {0} (A) x Pic ^ {0} (B)?

Since already many thanks

Flavio.

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–  Marty Mar 24 '11 at 20:55

In characteristic zero, yes. See Picard group, Fundamental group, and deformation I don't know about characteristic $p$.