Rusiru Gambheera

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20232026

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math.NT2026

An Equivariant Main Conjecture for Branched $Z_{p}$ -Towers of Finite Graphs and Applications

Rusiru Gambheera

Let $p$ be a prime and let $Y / X$ be a finite abelian branched cover of finite connected graphs. We consider a compatible branched $Z_{p}$ -tower above $Y$ whose total Galois g…

math.NT2025

Iwasawa theory for branched $Z_{p}$ -towers of finite graphs and Ihara zeta and $L$ -functions

Rusiru Gambheera, Daniel Vallières

We revisit the theory of Ihara $L$ -functions in the context initially studied by Bass and Hashimoto and more recently by Zakharov. In particular, we study if the Artin formalism is…

math.NT2025

Structure of (Fine) Mordell--Weil Groups

Rusiru Gambheera, Debanjana Kundu

In this article we study the algebraic structure of fine Mordell--Weil groups, plus/minus Mordell--Weil groups, Selmer groups, and plus/minus Selmer groups in the cyclotomic $\math…

math.NT2025

An Integral Equivariant Refinement of the Iwasawa Main Conjecture for Totally Real Fields

Rusiru Gambheera

For an abelian, CM extension $H / F$ of a totally real number field $F$ , we improve upon the reformulation of the Equivariant Tamagawa Number Conjecture for the Artin motive $h_{H/F}…

math.NT2025

Equivariant Iwasawa Theory for Ritter-Weiss Modules and Applications

Rusiru Gambheera, Cristian D. Popescu

We consider a finite, abelian, CM extension $H / F$ of a totally real number field $F$ , and construct a $Z_{p} [[G (H_{\infty} / F)]] -$ module $\nabla_{S}^{T} (H_{\infty})_{p}$ , where $p > 2$ i…

math.NT2024

On the $p$ -ranks of class groups of certain Galois extensions

Ufuoma Asarhasa, Rusiru Gambheera, Debanjana Kundu +2

Let $p$ be an odd prime, let $N$ be a prime with $N \equiv 1 (mod p)$ , and let $ζ_{p}$ be a primitive $p$ -th root of unity. We study the $p$ -rank of the class group of $\mathbb{Q}(ζ…

math.NT2024

Iwasawa theory for branched $Z_{p}$ -towers of finite graphs

Rusiru Gambheera, Daniel Vallières

We initiate the study of Iwasawa theory for branched $Z_{p}$ -towers of finite connected graphs. These towers are more general than what have been studied so far, since the…

math.NT2023

An unconditional main conjecture in Iwasawa theory and applications

Rusiru Gambheera, Cristian D. Popescu

We improve upon the recent keystone result of Dasgupta-Kakde on the $Z [G (H / F)]^{-}$ -Fitting ideals of certain Selmer modules $S e l_{S}^{T} (H)^{-}$ associated to an abelian, CM extensio…

An Equivariant Main Conjecture for Branched Zp​-Towers of Finite Graphs and Applications

Iwasawa theory for branched Zp​-towers of finite graphs and Ihara zeta and L-functions

Structure of (Fine) Mordell--Weil Groups

An Integral Equivariant Refinement of the Iwasawa Main Conjecture for Totally Real Fields

Equivariant Iwasawa Theory for Ritter-Weiss Modules and Applications

On the p-ranks of class groups of certain Galois extensions

Iwasawa theory for branched Zp​-towers of finite graphs

An unconditional main conjecture in Iwasawa theory and applications

An Equivariant Main Conjecture for Branched $Z_{p}$ -Towers of Finite Graphs and Applications

Iwasawa theory for branched $Z_{p}$ -towers of finite graphs and Ihara zeta and $L$ -functions

On the $p$ -ranks of class groups of certain Galois extensions

Iwasawa theory for branched $Z_{p}$ -towers of finite graphs