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The Heegner point Kolyvagin system

Published online by Cambridge University Press:  15 October 2004

Benjamin Howard
Benjamin Howard
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305, [email protected] Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
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Abstract

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In Bull. Soc. Math. France 115 (1987), 399–456, Perrin-Riou formulates a form of the Iwasawa main conjecture which relates Heegner points to the Selmer group of an elliptic curve defined over $\mathbb{Q}$, as one goes up the anticyclotomic $\mathbb{Z}_p$-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.

Keywords

Iwasawa theoryelliptic curvesHeegner pointsEuler systems11G0511R23
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 6 , November 2004 , pp. 1439 - 1472
Copyright
Foundation Compositio Mathematica 2004