Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.17003

Refined conjectures on Fitting ideals of BDP Selmer groups

Chan-Ho Kim·Aprameyo Pal·Jishnu Ray
View original source ↗Read source document ↗Export metadata ↓

Abstract

Under mild assumptions, we prove the strong main conjecture for BDP Selmer groups of elliptic curves with good reduction in the sense of Kurihara's refined Iwasawa theory. In particular, the structure of the initial Fitting ideal of BDP Selmer groups over finite subextensions in the anticyclotomic $\mathbb{Z}_p$-extension is determined by the values of the corresponding $p$-adic modular form at CM points.

Explore related subjects

math.NT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Chan-Ho Kim, Aprameyo Pal, Jishnu Ray. 2026-09-15. Refined conjectures on Fitting ideals of BDP Selmer groups. https://arxiv.org/abs/2609.17003

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On the factorisation of the $p$-adic Rankin-Selberg $L$-function in the supersingular case

Given a cusp form $f$ which is supersingular at a fixed prime $p$ away from the level, and a Coleman family $F$ through one of its $p$-stabilisations, we construct a $2$-variable meromorphic $p$-adic $L$-function for the symmetric square of $F$. We prove that this new $p$-adic $L$-function interpolates values of complex imprimitive symmetric square $L$-functions, for the various specialisations of the family $F$. We use this $p$-adic $L$-function to prove a $p$-adic factorisation formula, expressing the geometric $p$-adic $L$-function attached to the Rankin--Selberg convolution of $f$ with itself as a the product of the $p$-adic symmetric square $L$-function of $f$ and a Kubota-Leopoldt $L$-function. This extends a result of Dasgupta in the ordinary case.

math.NT↗
arXiv2026

Exceptional poles of archimedean Rankin-Selberg L-functions for irreducible generic representations of GL(n,R)

For irreducible generic representations $π_1$ and $π_2$ of $\operatorname{GL}_n(\mathbb R)$, we prove that the notions of exceptional pole of type $1$ and type $2$ coincide at every level. When both representations are in general position, we use this identification to express the Rankin--Selberg $L$-function $L(s,π_1\timesπ_2)$ in terms of the exceptional $L$-factors attached to the irreducible constituents of their derivatives.

math.NT↗