\(\ell\)-adic properties of certain modular forms. (English) Zbl 1160.11022

Moon, Hyunsuk; Taguchi, Yuichiro

Proc. Japan Acad., Ser. A 82, No. 7, 83-86 (2006).

The authors prove that Hecke-operators on certain spaces of \(\ell\)-adic modular forms (with \(\ell\in \{3,5,7\}\)) are topologically nilpotent. They then derive some arithmetic consequences of this result.

Reviewer: Stefan Kühnlein (Karlsruhe)

MSC:

11F33	Congruences for modular and \(p\)-adic modular forms
11F25	Hecke-Petersson operators, differential operators (one variable)
11F80	Galois representations
11S15	Ramification and extension theory

Keywords:

modular forms; Hecke-operators; mod \(\ell\) Galois representations; Serre’s \(\varepsilon\)-conjecture

References:

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