Abstract
An abelian surface of prime conductor is favorable if its 2-division field is an -extension over with ramification index 5 over . Let be favorable and let be a semistable abelian variety of dimension and conductor with filtered by copies of . We give a sufficient class field theoretic criterion on to guarantee that is isogenous to .
As expected from our paramodular conjecture, we conclude that there is one isogeny class of abelian surfaces for each conductor in . The general applicability of our criterion is discussed in the data section.
Citation
Armand Brumer. Kenneth Kramer. "Certain abelian varieties bad at only one prime." Algebra Number Theory 12 (5) 1027 - 1071, 2018. https://doi.org/10.2140/ant.2018.12.1027
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