## Some computations with Hecke rings and deformation rings. With an appendix by Amod Agashe and William Stein.(English)Zbl 1116.11310

Summary: In the proof by Wiles, completed by Taylor-Wiles, of the fact that all semistable elliptic curves over $$\mathbb Q$$ are modular, certain deformation rings play an important role. In this note, we explicitly compute these rings for the elliptic curve $$Y^2+XY=X^3-X^2-X-3$$ of conductor 142.

### MSC:

 11F80 Galois representations 11F11 Holomorphic modular forms of integral weight 11F25 Hecke-Petersson operators, differential operators (one variable)

### Keywords:

Hecke rings; deformation rings; modularity; elliptic curves

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### References:

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