Paramodular Abelian Varieties of Odd Conductor
By A. Brumer, Ken Kramer. 2010
87 citations recorded by the source corpus.
A precise and testable modularity conjecture for rational abelian surfaces A with trivial endomorphisms, End_Q A = Z, is presented. It is consistent with our examples, our non-existence results and recent work of C. Poor and D. S. Yuen on weight 2 Siegel paramodular forms. We obtain fairly precise information on ell-division fields of semistable abelian varieties A, mainly when A[ell] is reducible, by considering extension problems for groups schemes of small rank. Our general results imply, for instance, that the least prime conductor of an abelian surface is 277.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6b6478b710e14279e656d3c1ef8b3ce78882f95e
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Packet structure and paramodular forms (2017, background): “Siegel modular forms with respect to K(N) have received much attention in recent years because of their appearance in what has become known as the paramodular conjecture; see [3], [17].”