an:05123045
Zbl 1169.11314
Skinner, Christopher; Urban, Eric
On the \(p\)-adic deformations of certain automorphic representations
FR
J. Inst. Math. Jussieu 5, No. 4, 629-698 (2006).
00186922
2006
j
11G40 11F80 11F33 11F85 11F46
\(p\)-adic modular forms; Galois representations; Selmer groups; \(L\)-functions
Summary: By an entirely new method that makes use of \(p\)-adic deformations of automorphic representations of \(\mathrm{GSp}_{4}/\mathbb{Q}\), we prove that the \(p\)-adic Selmer group \(H^1_f(\mathbb{Q},V_f(k))\) associated to a modular form \(f\) of weight \(2k\) that is ordinary at \(p\) is infinite if the order of vanishing at \(k\) of the \(L\)-function of \(f\) is odd.
See also the authors' announcement in C. R., Math., Acad. Sci. Paris 335, No. 7, 581--586 (2002; Zbl 1024.11030).
Zbl 1024.11030