This is a little mysterious. Is the conjecture about to be proved? Would you be so kind as to share rumors or ideas you have on the topic?
I have a question. I think I understand the Tate conjecture (mostly) implies the Deligne-Beilinson conjecture, which I think generalize the BSD conjecture. Then: how much harder are the Tate conjectures thought to be than the BSD?
I think the Tate conjectures imply the Hodge conjecture too via some ideas of Deligne so I guess they are much harder than BSD.
Also what happened to Harada’s attempt at proving the standard conjectures? I have seen the paper was retracted. And why does the Tate conjecture (or the standard conjectures) for 1-motives imply it (resp. them) for all motives? That is, how does it imply that “the category of motives over finite fields is generated by abelian varieties”, as you quoted in this post: http://homotopical.wordpress.com/2009/02/04/update-on-haradas-proof/ ?
Well, don’t worry about ignoring my lazy questions, and thanks for all your work on this blog -and changing the “open link in new window” thing .