Perrin-Riou's main conjecture for elliptic curves at supersingular primes

2016/07/07 by Francesc Castella, Castella, Francesc, Xin Wan +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1607.02019

openalex publication_date 2016/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

In 1987, B. Perrin-Riou formulated a Heegner point main conjecture for elliptic curves at primes of ordinary reduction. In this paper, we formulate an analogue of Perrin-Riou's main conjecture for supersingular primes. We then prove this conjecture under mild hypotheses, and deduce from this result a Λ-adic extension of Kobayashi's p-adic Gross-Zagier formula, new cases of B.-D. Kim's doubly-signed main conjectures, and a strengthened version of Skinner's converse to the Gross-Zagier-Kolyvagin theorem for supersingular primes.

Cited by

• On the Tamagawa number conjecture for modular forms twisted by anticyclotomic Hecke characters

Related

• The main conjecture for CM elliptic curves at supersingular primes
• Iwasawa Main Conjecture for Heegner Points: Supersingular Case
• A formula of Perrin-Riou and characteristic power series of signed Selmer groups
• Plus/minus Heegner points and Iwasawa theory of elliptic curves at\n supersingular primes
• Anticyclotomic Iwasawa theory of abelian varieties of GL₂-type at non-ordinary primes II