On the Iwasawa theory of Cayley graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915044894179328 |
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| author | Ghosh, Sohan Ray, Anwesh |
| author_facet | Ghosh, Sohan Ray, Anwesh |
| contents | 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 $μ$- and $λ$-invariants. Additionally, we apply these insights to complete graphs, establishing conditions under which these invariants vanish. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Iwasawa theory of Cayley graphs Ghosh, Sohan Ray, Anwesh Number Theory Combinatorics Group Theory 11R23, 05C25, 05C31, 05C50 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 $μ$- and $λ$-invariants. Additionally, we apply these insights to complete graphs, establishing conditions under which these invariants vanish. |
| title | On the Iwasawa theory of Cayley graphs |
| topic | Number Theory Combinatorics Group Theory 11R23, 05C25, 05C31, 05C50 |
| url | https://arxiv.org/abs/2405.04361 |