PreprintCC BY 4.0arXiv
On Conjectures of μ-Invariant for Selmer Groups at p=2
Abstract
Let E be an elliptic curve define over ℚ. Further assume E has good ordinary reduction at p=2. In this article, we prove Greenberg's conjecture on the value of the algebraic Iwasawa μ-invariant when E has a rational isogeny of degree 2, and obtain a sharp absolute upper bound of the $2$-adic μ-invariants for all such curves. We also prove the vanishing of the algebraic μ-invariant of the fine Selmer group introduced by Coates and Sujatha at p=2.
Related
- Refined conjectures on Fitting ideals of BDP Selmer groups
- Bounding Selmer Groups of Superelliptic Jacobians via Class Groups
- Arithmetic statistics of isogeny Selmer groups associated to hyperelliptic curves
- Experiments on $3$-isogeny Selmer groups of elliptic curves with a $3$-torsion point
- Selmer groups of CM-twists of elliptic curves
BibTeX
@misc{lin2026conjectures,
title = {{On Conjectures of $μ$-Invariant for Selmer Groups at $p=2$}},
author = {Zichao Lin and Mulun Yin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31527},
eprint = {2609.31527},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31527},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Conjectures of μ-Invariant for Selmer Groups at p=2
AU - Zichao Lin
AU - Mulun Yin
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31527
UR - https://arxiv.org/abs/2609.31527
AB - Let E be an elliptic curve define over ℚ. Further assume E has good ordinary reduction at p=2. In this article, we prove Greenberg's conjecture on the value of the algebraic Iwasawa μ-invariant when E has a rational isogeny of degree 2, and obtain a sharp absolute upper bound of the $2$-adic μ-invariants for all such curves. We also prove the vanishing of the algebraic μ-invariant of the fine Selmer group introduced by Coates and Sujatha at p=2.
ER -