An extension of Wiles’ results. (English) Zbl 0917.11021

Diamond, Fred

Cornell, Gary (ed.) et al., Modular forms and Fermat’s last theorem. Papers from a conference, Boston, MA, USA, August 9–18, 1995. New York, NY: Springer. 475-489 (1997).

This is a helpful exposition of the author’s ‘On deformation rings and Hecke rings’ [Ann. Math. (2) 144, No. 1, 137-166 (1996; Zbl 0867.11032)], in which he proves the extension of Wiles’ result that it already suffices for an elliptic curve \(E\) over \(\mathbb Q\) to have good or multiplicative reduction at \(3\) and \(5\) in order then to show that \(E\) is modular.
For the entire collection see [Zbl 0878.11004].

Reviewer: A.J.van der Poorten (North Ryde)

MSC:

11G05	Elliptic curves over global fields
11F11	Holomorphic modular forms of integral weight

Keywords:

elliptic curve; modular curves

Citations:

Zbl 0867.11032