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Timeline for A question on BSD conjecture

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Aug 31, 2014 at 11:18 comment added user57657 You are right. I chase the proofs of Milne in jmilne.org/math/articles/1972a.pdf and "Arithmetic duality theorem". The two invariances are proved by comparing each ingredient one by one. So the equivalence on $p$-part should holds.
Aug 31, 2014 at 11:04 comment added Daniel Loughran Im guessing the answer is probably yes here, though I don't know references. I would recommend examining the proofs of invariance of BSD under Weil restriction and isogeny, and see if they can be adapted to this setting.
Aug 31, 2014 at 10:43 comment added user57657 Thanks. In a lot of cases, we know that the $p$-part of full BSD of $E$ and the quadratic twist of $E$ holds, by Skinner et. all. So what is the answer if we focus the question on the $p$-part of full BSD conjecture?
Aug 31, 2014 at 10:27 history answered Daniel Loughran CC BY-SA 3.0