Heegner Points and Exceptional Zeros of Garrett p-Adic L-Functions
نویسندگان
چکیده
Abstract This article proves a case of the p -adic Birch and Swinnerton–Dyer conjecture for Garrett L -functions (Bertolini et al. in On analogues -functions, 2021), imaginary dihedral exceptional zero setting extended analytic rank 4.
منابع مشابه
p-adic heights of Heegner points and Λ-adic regulators
Let E be an elliptic curve defined over Q. The aim of this paper is to make it possible to compute Heegner L-functions and anticyclotomic Λ-adic regulators of E, which were studied by Mazur-Rubin and Howard. We generalize results of Cohen and Watkins and thereby compute Heegner points of nonfundamental discriminant. We then prove a relationship between the denominator of a point of E defined ov...
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Introduction 1 1. Basic notions 6 1.1. Motives for rational and homological equivalence 6 1.2. Algebraic Hecke characters 7 1.3. The motive of a Hecke character 8 1.4. Deligne-Scholl motives 9 1.5. Modular parametrisations attached to CM forms 10 1.6. Generalised Heegner cycles and Chow-Heegner points 13 1.7. A special case 15 2. Chow-Heegner points over Cp 15 2.1. The p-adic Abel-Jacobi map 15...
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Introduction 2 1. Preliminaries 6 1.1. Algebraic modular forms 6 1.2. Modular forms over C 9 1.3. p-adic modular forms 11 1.4. Elliptic curves with complex multiplication 12 1.5. Values of modular forms at CM points 14 2. Generalised Heegner cycles 15 2.1. Kuga-Sato varieties 15 2.2. The variety Xr and its cohomology 18 2.3. Definition of the cycles 19 2.4. Relation with Heegner cycles and L-se...
متن کاملHeegner points, Stark-Heegner points, and values of L-series
Elliptic curves over Q are equipped with a systematic collection of Heegner points arising from the theory of complex multiplication and defined over abelian extensions of imaginary quadratic fields. These points are the key to the most decisive progress in the last decades on the Birch and Swinnerton-Dyer conjecture: an essentially complete proof for elliptic curves over Q of analytic rank ≤ 1...
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ژورنال
عنوان ژورنال: Milan Journal of Mathematics
سال: 2021
ISSN: ['1424-9286', '1424-9294']
DOI: https://doi.org/10.1007/s00032-021-00332-z