Katharina Müller

activity

20212026

most citedFine Selmer groups of congruent

p

-adic Galois representations

4 citations · 11 across the 9 of their papers we have counts for

collaborators

11 papers

math.NT2026

Iwasawa theory of (directed) Cayley graphs

Debanjana Kundu, Katharina Müller, Alexis newton +2

In this article, we prove the Defect Conjecture for Cayley graphs of abelian groups, dihedral groups, and groups of the form $\mathbb{Z}/p\mathbb{Z} \rtimes \mathbb{Z}/(p-1)\mathbb…

math.NT2023★ 2 cited

On towers of Isogeny graphs with full level structure

Antonio Lei, Katharina Müller

Let $p, q, l$ be three distinct prime numbers and let $N$ be a positive integer coprime to $pq l$ . For an integer $n \geq 0$ , we define the directed graph $X_{l}^{q} (p^{n} N)$ whose vertices a…

math.NT2023

On the non-commutative Iwasawa main conjecture for voltage covers of graphs

Sören Kleine, Katharina Müller

Let $p$ be a rational prime, and let $X$ be a connected finite graph. In this article we study voltage covers $X_{\infty}$ of $X$ attached to a voltage assignment $α$ which takes val…

math.NT2023

On the Zeta functions of supersingular isogeny graphs and modular curves

Antonio Lei, Katharina Müller

Let $p$ and $q$ be distinct prime numbers, with $q \equiv 1 (mod 12)$ . Let $N$ be a positive integer that is coprime to $pq$ . We prove a formula relating the Hasse--Weil zeta functi…

math.NT2023

On ordinary isogeny graphs with level structure

Antonio Lei, Katharina Müller

Let $l$ and $p$ be two distinct prime numbers. We study $l$ -isogeny graphs of ordinary elliptic curves defined over a finite field of characteristic $p$ , together with a level stru…

math.NT2023

On the Iwasawa invariants of BDP Selmer groups and BDP P-adic L-fucntions

Antonio Lei, Katharina Müller, Jiacheng Xia

Let $p$ be an odd prime. Let $f_{1}$ and $f_{2}$ be weight-two Hecke eigen-cuspforms with isomorphic residual Galois representations at $p$ . Greenberg--Vatsal and Emerton--Pollack--Wes…

math.NT2022★ 2 cited

On the growth of the Jacobian in $Z_{p}^{l}$ -voltage covers of graphs

Sören Kleine, Katharina Müller

We investigate the growth of the $p$ -part of the Jacobians in voltage covers of finite connected multigraphs, where the voltage group is isomorphic to $Z_{p}^{l}$ for some ${l…

math.NT2022

Fine Selmer groups of modular forms

Sören Kleine, Katharina Müller

We compare the Iwasawa invariants of fine Selmer groups of $p$ -adic Galois representations over admissible $p$ -adic Lie extensions of a number field $K$ to the Iwasawa invariants o…

math.NT2022

Asymptotic formula for Tate-Shafarevich groups of $p$ -supersingular elliptic curves over anticyclotomic extensions

Antonio Lei, Meng Fai Lim, Katharina Müller

Let $p \geq 5$ be a prime number and $E / Q$ an elliptic curve with good supersingular reduction at $p$ . Under the generalized Heegner hypothesis, we investigate the $p$ -prima…

math.NT2021★ 3 cited

Fine Selmer groups and ideal class groups

Sören Kleine, Katharina Müller

Let $K_{\infty} / K$ be a uniform $p$ -adic Lie extension. We compare several arithmetic invariants of Iwasawa modules of ideal class groups on the one side and fine Selmer groups of ab…

math.NT2021★ 4 cited

Fine Selmer groups of congruent $p$ -adic Galois representations

Sören Kleine, Katharina Müller

We compare the Pontryagin duals of fine Selmer groups of two congruent $p$ -adic Galois representations over admissible pro- $p$ , $p$ -adic Lie extensions $K_{\infty}$ of number fields…

Iwasawa theory of (directed) Cayley graphs

On towers of Isogeny graphs with full level structure

On the non-commutative Iwasawa main conjecture for voltage covers of graphs

On the Zeta functions of supersingular isogeny graphs and modular curves

On ordinary isogeny graphs with level structure

On the Iwasawa invariants of BDP Selmer groups and BDP P-adic L-fucntions

On the growth of the Jacobian in Zpl​-voltage covers of graphs

Fine Selmer groups of modular forms

Asymptotic formula for Tate-Shafarevich groups of p-supersingular elliptic curves over anticyclotomic extensions

Fine Selmer groups and ideal class groups

Fine Selmer groups of congruent p-adic Galois representations

On the growth of the Jacobian in $Z_{p}^{l}$ -voltage covers of graphs

Asymptotic formula for Tate-Shafarevich groups of $p$ -supersingular elliptic curves over anticyclotomic extensions

Fine Selmer groups of congruent $p$ -adic Galois representations