Paramodular Abelian Varieties of Odd Conductor
| Autor: | Brumer, Armand, Kramer, Kenneth |
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| Rok vydání: | 2010 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Frank Calegari was kind enough to point out an oversight in the paramodular conjecture stated in earlier versions. We added Section 8, in which we propose a modified conjecture and show that the modification concerns a rare phenomenon. The numerical evidence in the appendix applies equally to the modified conjecture |
| Databáze: | arXiv |
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