Jon Aycock
Published 2024-05-21Version 1
The Jacobian is an algebraic invariant of a graph which is often seen in analogy to the class group of a number field. In particular, there have been multiple investigations into the Iwasawa theory of graphs with the Jacobian playing the role of the class group. In this paper, we construct an Iwasawa module related to the Jacobian of a $\mathbb{Z}_p$-tower of connected graphs, and give examples where we use this to compute asymptotic sizes of the Jacobians in this tower.
Comments: 11 pages, 2 figures
On the $16$-rank of class groups of $\mathbb{Q}(\sqrt{-3p})$ for primes $p$ congruent to $1$ modulo $4$
On a conjecture for $\ell$-torsion in class groups of number fields: from the perspective of moments
On Iwasawa Theory over Function Fields
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