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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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"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
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What's the reason for the downvotes? Please explain. –  Makoto Kato Aug 13 '12 at 0:39
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@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
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@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

1 Answer 1

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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