2004/10/15 by Benjamin Howard · 4 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Combinatorics #Computer science #Conjecture #Divisibility rule #Elliptic curve #Euler equations #Euler system #Euler's formula #Extension (predicate logic) #Geometry #Group (periodic table) #Iwasawa theory #Mathematical analysis #Mathematics #Physics #Point (geometry) #Pure mathematics #Quadratic equation #Quantum mechanics #Rank (graph theory)
paper · pdf · doi:10.1112/s0010437x04000569
published in Compositio Mathematica 140(6), 1439-1472 (Cambridge University Press)
openalex publication_date 2004/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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 -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.