Yves Hellegouarch

Yves Hellegouarch (born September 18, 1936 ) is a French mathematician who deals with number theory. He was a professor at Caen University .

Hellegouarch studied from 1957 at the École normal supérieure (Paris) with a degree in mathematics.

In 1969, Hellegouarch introduced the elliptic curves E (a, b), later named after Gerhard Frey , constructed from the solutions of the Fermat equation :

${\displaystyle y^{2}=x(x-a^{p})(x-b^{p})}$

above the rational numbers. He also showed that they (or their torsion points of order p) had some very special properties. Hellegouarch had previously investigated the rational points of finite order (torsion points) on elliptic curves and, like independently Vadim Andrejewitsch Demjanenko, recognized that the existence of a point of order resulted in a nontrivial solution of the Fermat equation of the p-th degree. ${\displaystyle 2p^{2}}$

Gerhard Frey (who knew the works of Hellegouarch) recognized in 1986 that they were a counterexample to the Taniyama-Shimura conjecture of the modularity of elliptic curves over the rational numbers, which was proven by Ken Ribet , who also did that of Jean-Pierre Serre on this Purpose established epsilon conjecture proved. That was the starting point of Andrew Wiles' 1994 evidence .

Hellegouarch reported on the curves in a lecture at the Journées Arithmétiques de Bordeaux 1969 (not published), in an article in the Comptes Rendus Acad. Sci. 1971, extensively in his dissertation at the University of Besançon 1972 and in an essay in Acta Arithmetica.

In 1997 he wrote a book on the mathematical background of the proof of the Fermat conjecture by Wiles. He also dealt with Drinfeld modules.

He had been at Caen University since 1970, where he retired in 2000. He also taught at the universities in Orsay, Besançon and Caen.

He plays the cello at a high level and has also published on mathematical (number theoretical) aspects of scales. He studied at the Conservatoire national supérieur de musique et de danse de Paris (CNSM) and won first prize in cello and a medal in chamber music.

Fonts

• Invitation aux mathématiques de Fermat-Wiles, Paris, Masson 1997, 2nd edition Dunod 2001
  • English translation: Invitation to the Mathematics of Fermat-Wiles, Academic Press 2002
• Fermat enfin démontré, Pour la Science, February 1996
• Points d'ordre fini des variétés abéliennes de dimension un , Mémoires de la Société Mathématique de France, 25 (1971), 107-112, numdam
• Etude des points d'ordre fini des variétés abéliennes de dimension un définies sur un anneau principal , Journal for Pure and Applied Mathematics, Volume 244, 1970, pp. 20-36

Web links

• BNF
• Biography at Canal U

Individual evidence

1. ↑ Hellegouarch, Pour la Science, February 1996, see literature
2. ^ Letter from Hellegouarch to the Gazette des Mathematiciens 2000 ( Memento of the original dated February 4, 2012 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
3. ^ Points d'ordre fini sur les courbes elliptiques , Comptes Rendus Acad. Sci., Vol. 273, 1971, 540-543
4. ↑ Courbes elliptiques et équation de Fermat , 1972
5. ^ Points d'ordre sur les courbes elliptiques ${\displaystyle 2p^{h}}$ , Acta Arithmetica, Volume 26, 1975, pp. 253-263, pdf
6. ↑ Hellegouarch, Gammes naturelles I, Gazette des Mathématiciens, May 1999