2015/12/31 by Florian Sprung, Sprung, Florian
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1512.09362
To appear in 'Research in Number Theory,' volume 1, issue 1. The generalization of the theorems of Kurihara and Pollack is new, while the p-adic BSD conjectures in terms of the integral p-adic L-functions supersedes part of an earlier arxiv submission [arXiv:1211.1352], which is being withdrawn
arxiv created 2015/12/31 · openalex publication_date 2015/12/31 · arxiv updated 2016/01/01 · openalex created_date 2022/09/25 · openalex updated_date 2026/07/28
Given an elliptic curve E and a prime p of (good) supersingular reduction, we formulate p-adic analogues of the Birch and Swinnerton-Dyer conjecture using a pair of Iwasawa functions L^\sharp(E,T) and L^\flat(E,T). They are equivalent to the conjectures of Perrin-Riou and Bernardi. We also generalize work of Kurihara and Pollack to give a criterion for positive rank in terms of the value of the quotient between these functions, and derive a result towards a non-vanishing conjecture. We also generalize a conjecture of Kurihara and Pollack concerning the greatest common divisor of the two functions to the general supersingular case.