The Heegner point Kolyvagin system

Details The Heegner point Kolyvagin system The Heegner point Kolyvagin system

2012-02-28

arxiv.org/abs/1202.6340v1

Compos. Math. 141, No 6 (2004), 1439-1472

Mathematics

Number Theory

Scientific paper

Perrin-Riou has formulated a form of the Iwasawa main conjecture, which relates Heegner points to the Selmer group of an elliptic curve as one goes up the anticyclotomic Z_p extension of a quadratic imaginary field K. Building on the earlier work of Bertolini on this conjecture, and making use of the recent work of Mazur and Rubin on Kolyvagin's theory of Euler systems, we prove one divisibility of Perrin-Riou's conjectured equality. As a consequence, one obtains an upper bound on the rank of the Mordell-Weil group E(K) in terms of Heegner points.

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