Growth of Selmer groups of Hilbert modular forms over ring class fields. (English) Zbl 1236.11047
Summary: We prove non-trivial lower bounds for the growth of ranks of Selmer groups of Hilbert modular forms over ring class fields and over certain Kummer extensions, by establishing first a suitable parity result.
MSC:
| 11F41 | Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces |
| 11F66 | Langlands \(L\)-functions; one variable Dirichlet series and functional equations |
| 11F80 | Galois representations |
| 11G18 | Arithmetic aspects of modular and Shimura varieties |
