Joint IAS/Princeton University Number Theory Seminar

We prove a B-SD conjecture for elliptic curves (for the \(p^\infty\) Selmer groups with arbitrary rank) a la Mazur-Tate and Darmon in anti-cyclotomic setting, for certain primes \(p\). This is done, among other things, by proving a conjecture of Kolyvagin in 1991 on \(p\)-indivisibility of (derived) Heegner points over ring class fields.