On the growth of the Jacobians in ℤ p l -voltage covers of graphs
Sören Kleine, Katharina Müller
Source abstract
We investigate the growth of the p -part of the Jacobians in voltage covers of finite connected graphs, where the voltage group is isomorphic to ℤ p l for some l ≥ 2 , and we study analogues of a conjecture of Greenberg on the growth of class numbers in multiple ℤ p -extensions of number fields. Moreover we prove an Iwasawa main conjecture in this setting, and we study the variation of (generalised) Iwasawa invariants as one runs over the ℤ p l -covers of a fixed finite graph X . We discuss many examples; in particular, we construct examples with non-trivial Iwasawa invariants.
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