A higher Gross–Zagier formula and the structure of Selmer groups
A higher Gross–Zagier formula and the structure of Selmer groups
We describe a Kolyvagin system-theoretic refinement of Gross–Zagier formula by comparing Heegner point Kolyvagin systems with Kurihara numbers when the root number of a rational elliptic curve <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E"> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding="application/x-tex">E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> over an imaginary quadratic field <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper …