Links between stable elliptic curves and certain diophantine equations. (English) Zbl 0586.10010

Frey, Gerhard

Ann. Univ. Sarav., Ser. Math. 1, No. 1, 40 p. (1986).

The paper under review relates solutions of the Fermat equation \(X^p+Y^p=Z^p\) to elliptic curves. To \((x,y,z)\) corresponds the elliptic curve \(U^2=V(V-x^p)(V-z^p)\). He then shows that this elliptic curve has many remarkable properties, so that one might hope to show that it does not exist. He explains several approaches on how to do this, which lead to quite plausible conjectures which would imply Fermat’s Last Theorem.

Reviewer: Gerd Faltings (Wuppertal/Princeton)

MSC:

11D41	Higher degree equations; Fermat’s equation
11G05	Elliptic curves over global fields

Keywords:

Fermat equation; elliptic curves; Fermat’s Last Theorem