I want to study Mumford's Abelian Varieties in the coming winter break. I tried to study it before, but I didn't find my self really understanding(or memorizing) too much. I guess a better and more solid way to learn something is to go over many exercises. So I'm asking for some exercises(or problems?) on abelian varieties, it would be nice if I can get them online. Thanks in advance.
And about the exercises: I wish it would be kind of like the ones in Hartshorne, so that I can solve them if I understand the material well. And not too hard, I guess I'm not looking for some research level questions... Also I wish those exercises may focus more on the algebraic/arithmetic side. I know the description above might seem a little picky, I'd be very appreciated if anyone has any idea or source about this, thanks again in advance...