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A refined non-vanishing of the -adic logarithm of a rational point on an abelian variety
Ashay Burungale, Christopher Skinner, Xin Wan
Inspired by a beautiful formula of Bertolini, Darmon, and Prasanna -- the oft-termed BDP formula -- we address questions about the non-vanishing of non-torsion points under -adi…
Non-vanishing of Kolyvagin systems and Iwasawa theory
Ashay Burungale, Francesc Castella, Giada Grossi +1
Let be an elliptic curve and an odd prime. In 1991 Kolyvagin conjectured that the system of cohomology classes for torsion quotients of the -adic Tate module…
Base change and Iwasawa Main Conjectures for
Ashay Burungale, Francesc Castella, Christopher Skinner
Let be an elliptic curve defined over of conductor , an odd prime of good ordinary reduction such that is an irreducible Galois module, and an im…
Zeta elements for elliptic curves and applications
Ashay Burungale, Christopher Skinner, Ye Tian +1
Let be an elliptic curve defined over with conductor and a prime. Let be an imaginary quadratic field with split. We prove the existence of…