From the Taniyama-Shimura conjecture to Fermat’s last theorem. (English) Zbl 0726.14015

Ribet, Kenneth A.

Ann. Fac. Sci. Toulouse, V. Sér., Math. 11, No. 1, 116-139 (1990).

The author outlines a proof of his “conjecture \(\epsilon\),” namely that the Taniyama-Shimura-Weil conjecture implies Fermat’s conjecture (by applying it to G. Frey’s elliptic curve). What is new is that he gives a simplified procedure, using the bad reduction at the prime two of the elliptic curve. He thus avoids the use of another auxiliary prime.

Reviewer: G.Faltings (Princeton)

MSC:

14G05	Rational points
14H52	Elliptic curves
11F80	Galois representations
11G05	Elliptic curves over global fields
11D41	Higher degree equations; Fermat’s equation
14G35	Modular and Shimura varieties

Keywords:

Taniyama-Shimura-Weil conjecture; Fermat’s conjecture; G. Frey’s elliptic curve; reduction at the prime two

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