Author

Katharina Müller

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Preprint Sep 2026

Iwasawa theory of (directed) Cayley graphs

In this article, we prove the Defect Conjecture for Cayley graphs of abelian groups, dihedral groups, and groups of the form $\mathbb{Z}/p\mathbb{Z} \rtimes \mathbb{Z}/(p-1)\mathbb{Z}$ where $p\geq 3$ is a prime. We also compute the Iwasawa invariants of the Bowen--Franks groups associated with these graphs in several...

Debanjana Kundu, Katharina Müller, A. Newton et al. · 0 citations

Preprint Aug 2026

Modularity theorems for Eisenstein congruences in prime-power level

Let $p, N \geq 5$ be primes such that $N \equiv 1 \bmod p$. We prove modularity theorems at levels $N$ and $N^2$, showing that suitable Eisenstein localizations of the weight-$2$ $p$-adic Hecke algebra at these levels are isomorphic to certain natural quotients of a universal pseudodeformation ring. This universal ring...

Jaclyn Lang, Katharina Müller, Bharathwaj Palvannan · 1 citation