We investigate the growth of the -part of the Jacobians in voltage covers of finite connected graphs, where the voltage group is isomorphic to for some , and we study analogues of a conjecture of Greenberg on the growth of class numbers in multiple -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 -covers of a fixed finite graph . We discuss many examples; in particular, we construct examples with non-trivial Iwasawa invariants.
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Keywords: Voltage cover of a graph, Greenberg’s conjecture, Iwasawa main conjecture, (generalised) Iwasawa invariants
Kleine, Sören 1; Müller, Katharina 2
@article{ALCO_2024__7_4_1011_0, author = {Kleine, S\"oren and M\"uller, Katharina}, title = {On the growth of the {Jacobians} in $\mathbb{Z}_p^l$-voltage covers of graphs}, journal = {Algebraic Combinatorics}, pages = {1011--1038}, publisher = {The Combinatorics Consortium}, volume = {7}, number = {4}, year = {2024}, doi = {10.5802/alco.366}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.366/} }
TY - JOUR AU - Kleine, Sören AU - Müller, Katharina TI - On the growth of the Jacobians in $\mathbb{Z}_p^l$-voltage covers of graphs JO - Algebraic Combinatorics PY - 2024 SP - 1011 EP - 1038 VL - 7 IS - 4 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.366/ DO - 10.5802/alco.366 LA - en ID - ALCO_2024__7_4_1011_0 ER -
%0 Journal Article %A Kleine, Sören %A Müller, Katharina %T On the growth of the Jacobians in $\mathbb{Z}_p^l$-voltage covers of graphs %J Algebraic Combinatorics %D 2024 %P 1011-1038 %V 7 %N 4 %I The Combinatorics Consortium %U https://alco.centre-mersenne.org/articles/10.5802/alco.366/ %R 10.5802/alco.366 %G en %F ALCO_2024__7_4_1011_0
Kleine, Sören; Müller, Katharina. On the growth of the Jacobians in $\mathbb{Z}_p^l$-voltage covers of graphs. Algebraic Combinatorics, Volume 7 (2024) no. 4, pp. 1011-1038. doi : 10.5802/alco.366. https://alco.centre-mersenne.org/articles/10.5802/alco.366/
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