Frey, Gerhard The way to the proof of Fermat’s last theorem. (English) Zbl 1201.11001 Ann. Fac. Sci. Toulouse, Math. (6) 18, Spec. Iss., 5-23 (2009). The author explains, why Wiles’ result on the Shimura-Tanyjama-Weil conjecture implies Fermat’s Last Theorem. Reviewer: Stefan Kühnlein (Karlsruhe) MSC: 11-03 History of number theory 01A60 History of mathematics in the 20th century 11D41 Higher degree equations; Fermat’s equation 11F80 Galois representations 11G05 Elliptic curves over global fields Keywords:Fermat’s Last Theorem; elliptic curves; Galois representations PDFBibTeX XMLCite \textit{G. Frey}, Ann. Fac. Sci. Toulouse, Math. (6) 18, 5--23 (2009; Zbl 1201.11001) Full Text: DOI EuDML Link References: [1] Modular forms and Fermat’s Last Theorem; ed. G. Cornell, J.H. Silverman, G. Stevens, New York (1997). · Zbl 0878.11004 [2] Frey (G.).— Some remarks concerning points of finite order on elliptic curves over global fields; Arkiv för Mat. 15, p. 1-19 (1977). · Zbl 0348.14018 [3] Frey (G.).— Links between stable elliptic curves and certain Diophantine equations; Ann. Univ. Saraviensis, 1, p. 1-40 (1986). · Zbl 0586.10010 [4] Frey (G.).— On ternary equations of Fermat type and relations with elliptic curves; in [MF], 527-548. · Zbl 0976.11027 [5] Hellegouarch (Y.).— Points d’ordre \(2^{p^h}\) sur les courbes elliptiques; Acta Arith. 26, p. 253-263 (1975). · Zbl 0264.14007 [6] Mazur (B.).— Modular curves and the Eisenstein ideal; Publ. math. IHES 47, p. 33-186 (1977). · Zbl 0394.14008 [7] Ribenboim (P.).— 13 Lectures on Fermat’s Last Theorem; New York (1982). · Zbl 0456.10006 [8] Ribet (K.).— On modular representations of \(Gal(\overline{{\mathbb{Q}}}/\mathbb{Q})\) arising from modular forms; Inv. Math. 100, p. 431-476 (1990). · Zbl 0773.11039 [9] Roquette (P.).— Analytic theory of elliptic functions over local fields; Hamb. Math. Einzelschriften, Neue Folge-Heft 1, Vandenhoeck und Ruprecht, Göttingen (1969). · Zbl 0194.52002 [10] Serre (J.-P.).— Propriétés galoisiennes des points d’ordre finis des courbes elliptiques; Inv. Math. 15, p. 259-331 (1972). · Zbl 0235.14012 [11] Serre (J.-P.).— Sur les représentations modulaires de degré 2 de \(G(\overline{{\mathbb{Q}}}/\mathbb{Q})\); Duke Math. J. 54, p. 179-230 (1987). · Zbl 0641.10026 [12] Silverman (J.H.).— The Arithmetic of Elliptic Curves; GTM 106, Berlin and New York (1986). · Zbl 0585.14026 [13] Tate (J.).— The arithmetic of elliptic curves; Inv. Math. 23, p. 179-206 (1974). · Zbl 0296.14018 [14] Taylor (R.), Wiles (A.).— Ring theoretic properties of certain Hecke algebras; Annals of Math. 141, p. 553-572 (1995). · Zbl 0823.11030 [15] Wiles (A.).— Modular elliptic curves and Fermat’s Last Theorem; Annals of Math. 142, p. 443-551 (1995). · Zbl 0823.11029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.