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Can anyone give me a precise information or formulation of Birch and Swinnerton-Dyer conjecture for Jacobians -- I mean for Albanese varieties. Any reference to useful links or expository articles, or any material is appreciated.

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    @MakotoKato : Yes sir, it happened to me many times. Many people here are filled with grudges and I think you too know it and experienced it . But Thank you for your response. We never care about the reputation, and we should make it explicit. Either they must change or we must. I think the latter is better.2012-08-13

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Every abelian variety is an Albanese variety: in fact, every abelian variety is its own Albanese variety. Thus asking about BSD "for Albanese varieties" is equivalent to asking about BSD for all abelian varieties: i.e., the general case.

The story might change if you want to restrict the class of varieties $V$ you want to take the Albanese variety of. In particular one is probably in slightly better shape looking at Jacobians -- i.e., Albanese varieties of curves -- than arbitrary abelian varieties, although in any case very little is known about BSD for anything but elliptic curves over $\mathbb{Q}$ of analytic rank at most $1$.