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arXiv · 2405.04361

On the Iwasawa theory of Cayley graphs

Sohan Ghosh·Anwesh Ray
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Abstract

This paper explores Iwasawa theory from a graph theoretic perspective, focusing on the algebraic and combinatorial properties of Cayley graphs. Using representation theory, we analyze Iwasawa-theoretic invariants within $\mathbb{Z}_\ell$-towers of Cayley graphs, revealing connections between graph theory, number theory, and group theory. Key results include the factorization of associated Iwasawa polynomials and the decomposition of $\mu$- and $\lambda$-invariants. Additionally, we apply these insights to complete graphs, establishing conditions under which these invariants vanish.

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BibTeXRIS

Sohan Ghosh, Anwesh Ray. 2024-05-07. On the Iwasawa theory of Cayley graphs. https://doi.org/10.1007/s40687-024-00487-2

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