Iwasawa Theory of Jacobians of Graphs
Algebraic Combinatorics, Volume 5 (2022) no. 5, pp. 827-848.

The Jacobian group (also known as the critical group or sandpile group) is an important invariant of a finite, connected graph X; it is a finite abelian group whose cardinality is equal to the number of spanning trees of X (Kirchhoff’s Matrix Tree Theorem). A specific type of covering graph, called a derived graph, that is constructed from a voltage graph with voltage group G is the object of interest in this paper.

Towers of derived graphs are studied by using aspects of classical Iwasawa Theory (from number theory). Formulas for the orders of the Sylow p-subgroups of Jacobians in an infinite voltage p-tower, for any prime p, are obtained in terms of classical μ and λ invariants by using the decomposition of a finitely generated module over the Iwasawa Algebra.

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DOI: 10.5802/alco.225
Keywords: Jacobian group, Iwasawa Theory, Laplacian, voltage graph, Picard group
Gonet, Sophia R. 1

1 Rutgers University Mathematics Department 110 Frelinghuysen Rd. Piscataway NJ 08854
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Gonet, Sophia R. Iwasawa Theory of Jacobians of Graphs. Algebraic Combinatorics, Volume 5 (2022) no. 5, pp. 827-848. doi : 10.5802/alco.225. https://alco.centre-mersenne.org/articles/10.5802/alco.225/

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