Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 5 (2018), 1027-1071.
Certain abelian varieties bad at only one prime
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.
Algebra Number Theory, Volume 12, Number 5 (2018), 1027-1071.
Received: 1 September 2016
Revised: 20 August 2017
Accepted: 23 October 2017
First available in Project Euclid: 14 August 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11G10: Abelian varieties of dimension > 1 [See also 14Kxx]
Secondary: 11R37: Class field theory 11S31: Class field theory; $p$-adic formal groups [See also 14L05] 14K15: Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx]
Brumer, Armand; Kramer, Kenneth. Certain abelian varieties bad at only one prime. Algebra Number Theory 12 (2018), no. 5, 1027--1071. doi:10.2140/ant.2018.12.1027. https://projecteuclid.org/euclid.ant/1534212096