Michel Raynaud

Michel Raynaud (born June 16, 1938 in Riom ; † March 10, 2018 ) was a French mathematician who dealt with algebraic geometry .

Life

Raynaud studied from 1958 at the École normal supérieure and in the 1960s was a student and close collaborator of Alexandre Grothendieck , with whom he also received his doctorate in 1968 (Faisceaux amples sur les schémas en groupes et les espaces homogènes) . From 1967 he was a professor at the University of Paris-Süd in Orsay . In 1983 he proved the Manin-Mumford conjecture that the Jacobi variety of a curve can only have a finite number of points of finite order (except in the case ). Fyodor Alexejewitsch Bogomolow already achieved partial results there and later, Ehud Hrushovski and Jonathan Pila and Umberto Zannier provided theoretical model evidence. ${\displaystyle J}$ ${\displaystyle C}$ ${\displaystyle C=J}$

In 1987 he received the Prix ​​Ampère of the Académie des Sciences and in 1995 the Cole Prize with David Harbater for solving Abhyankar's conjecture from 1957, which Raynaud proved for the special case of the (affine) straight line. The conjecture asks about the possible Galois groups of a superposition of a curve over a body of the characteristic, branched at points . Abhyankar hypothesized that G is a Galois group if and only if the number of producers of (where the subgroup of produced by all - Sylow- subgroups of is the same) , where the gender denotes the curve. ${\displaystyle G}$ ${\displaystyle t}$ ${\displaystyle C}$ ${\displaystyle p}$ ${\displaystyle G/p(G)}$ ${\displaystyle p(G)}$ ${\displaystyle p}$ ${\displaystyle G}$ ${\displaystyle G}$ ${\displaystyle 2g+t}$ ${\displaystyle g}$

Raynaud has been a corresponding member of the French Academy of Sciences since 1994 . In 1970 he was invited speaker at the International Congress of Mathematicians in Nice (Variétés abélienne et géométrie rigide) .

He was married to the mathematician Michèle Raynaud (* 1938), who also received her doctorate from Grothendieck (1972, University of Paris VII, Théorèmes de Lefschetz en cohomologie cohérente et en cohomologie étale ) and worked at the SGA (Séminaire de géométrie algébrique) at Grothendieck .

Fonts

• Faisceaux amples sur les schémas en groupes et les espaces homogènes. Springer, 1970.
• Anneaux Locaux Henseliens. Springer, 1970.
• with Siegfried Bosch , Werner Lütkebohmert: Néron Models. In: Results of mathematics and its border areas. Springer, 1990.
• Courbes sur une variété abélienne et points de torsion. In: Inventiones Mathematicae. 71, 1983, 207-233. (Manin-Mumford conjecture)
• Sous-variétés d'une variété abélienne et points de torsion. In: Arithmetic and Geometry (Shafarevich volume). Birkhäuser, 1983.
• Around the Mordell conjecture for function fields and a conjecture of Serge Lang. In: Algebraic Geometry. Lecture Notes in Mathematics 1016, Springer, 1983, 1–19.

literature

• Luc Illusie : Michael Raynaud 1938–2018, Notices of the AMS, January 2019

Web links

• Raynaud at the French Academy of Sciences

Individual evidence

1. ^ Décès de Michel Raynaud , accessed on March 14, 2018
2. ↑ Michel Raynaud in the Mathematics Genealogy Project (English)
3. ↑ Raynaud: Sous-variétés d'une variété abélienne et points de torsion. In: Michael Artin , John T. Tate (Editor): Arithmetic and geometry. Papers dedicated to IR Shafarevich on the occasion of his sixth birthday. Volume 1, Progress in Mathematics 35, Birkhäuser, 1983, pp. 327-352
4. ↑ Raynaud: Revêtements de la droite affine en caractéristique . ${\displaystyle p>0}$In: Inventiones Mathematicae . Vol. 116, 1994, pp. 425-462.
5. ↑ projective line minus one point
6. ↑ Page from Raynaud at the Academie des Sciences ( Memento des Originals from August 10, 2011 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. .  
7. ↑ Bull. Soc. Math. France, Memoirs No. 41, 1975, Mathematics Genealogy Project