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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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closed as too broad by Jonas Meyer, Donkey_2009, Aaron Maroja, TMM, quid Mar 22 '15 at 19:08

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

"any reference to useful links or expository articles,or any material is appreciated thanks a lot" - you have tried searching on Google Scholar, I presume? – J. M. May 9 '11 at 17:50
What's the reason for the downvotes? Please explain. – Makoto Kato Aug 13 '12 at 0:39
@MakotoKato : Its common in MO and Math.SE , to down-vote without any reason. I have shouted, requested , begged and did everything , to explain the reason for down voting , but no one cared. Apart from reducing the reputation, if users post the reason its useful for constructing good questions next time. But I don't know why everyone is not that CIVIC. Thank you sir. – Iyengar Aug 13 '12 at 4:22
@Iyengar I agree with you. I don't think your question deserves downvotes. The only reason I can think of is that they have grudges or jealousy on you. That's a despicable thing to do if that is the case, IMO. – Makoto Kato Aug 13 '12 at 6:58
@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. – Iyengar Aug 13 '12 at 8:25
up vote 11 down vote accepted

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 $1$.

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