Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
157 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Algebraic structure and characteristic ideals of fine Mordell--Weil groups and plus/minus Mordell--Weil groups (2307.12054v1)

Published 22 Jul 2023 in math.NT

Abstract: Given an elliptic curve defined over a number field $F$, we study the algebraic structure and prove a control theorem for Wuthrich's fine Mordell--Weil groups over a $\mathbb{Z}_p$-extension of $F$, generalizing results of Lee on the usual Mordell--Weil groups. In the case where $F=\mathbb{Q}$, we show that the characteristic ideal of the Pontryagin dual of the fine Mordell--Weil group over the cyclotomic $\mathbb{Z}_p$-extension coincides with Greenberg's prediction for the characteristic ideal of the dual fine Selmer group. If furthermore $E$ has good supersingular reduction at $p$ with $a_p(E)=0$, we generalize Wuthrich's fine Mordell--Weil groups to define "plus and minus Mordell--Weil groups". We show that the greatest common divisor of the characteristic ideals of the Pontryagin duals of these groups coincides with Kurihara--Pollack's prediction for the greatest common divisor of the plus and minus $p$-adic $L$-functions.

Citations (5)

Summary

We haven't generated a summary for this paper yet.