# Michel Raynaud

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French mathematician

Not to be confused with his wife and colleague, [Michèle Raynaud](/source/Mich%C3%A8le_Raynaud).

Michel Raynaud Born (1938-06-16)16 June 1938 Riom, France Died 10 March 2018(2018-03-10) (aged 79) Rueil-Malmaison, France Alma mater Paris-Sud 11 University Known for Abhyankar's conjecture Manin–Mumford conjecture Raynaud surface Raynaud's isogeny theorem Awards Cole Prize (1995) Prize Ampère (1987) Scientific career Fields Mathematics Institutions Paris-Sud 11 University Doctoral advisor Alexander Grothendieck

**Michel Raynaud** (French: [\[ʁɛno\]](https://en.wikipedia.org/wiki/Help:IPA/French); 16 June 1938 – 10 March 2018[1]) was a French [mathematician](/source/Mathematician) working in [algebraic geometry](/source/Algebraic_geometry)[2] and a professor at [Paris-Sud 11 University](/source/Paris-Sud_11_University).

## Early life and education

He was born in [Riom](/source/Riom), France as a single son to a modest household. His father was a carpenter and his mother cleaned houses.[3] He attended the local primary school at [Châtel Guyon](/source/Ch%C3%A2tel-Guyon) and Riom, and attended high school at the boarding school in [Clermont-Ferrand](/source/Clermont-Ferrand).[3]

Raynaud entered the [École normale supérieure](/source/%C3%89cole_normale_sup%C3%A9rieure_(Paris)) where he studied from 1958 to 1962, while being first of the class in the "agrégation" exam where the new high school teachers were selected in 1961.[3] In 1962, he entered the [French National Centre for Scientific Research](/source/French_National_Centre_for_Scientific_Research) where he studied together with his future wife [Michèle Chaumartin](/source/Mich%C3%A8le_Chaumartin). Both had the same doctoral advisor in [Alexander Grothendieck](/source/Alexander_Grothendieck). Raynaud received his doctoral degree in 1967.[3]

## Career

Raynaud was hired as professor at the [Orsay Faculty of Sciences](/source/Orsay_Faculty_of_Sciences) in Paris where he was employed until 2001, when he retired.[3]

Raynaud died on 10 March 2018 in [Rueil-Malmaison](/source/Rueil-Malmaison), France.[1]

## Research

In 1983, Raynaud published a proof of the [Manin–Mumford conjecture](/source/Manin%E2%80%93Mumford_conjecture).[4] In 1985, he proved [Raynaud's isogeny theorem](/source/Raynaud's_isogeny_theorem) on [Faltings heights](/source/Faltings_height) of isogenous [elliptic curves](/source/Elliptic_curves).[5] With [David Harbater](/source/David_Harbater) and following the work of [Jean-Pierre Serre](/source/Jean-Pierre_Serre), Raynaud proved [Abhyankar's conjecture](/source/Abhyankar's_conjecture) in 1994.[6][7][8]

The [Raynaud surface](/source/Raynaud_surface) was named after him by William E. Lang in 1979.[9][10]

## Honors and awards

In 1970 Raynaud was an [invited speaker](/source/List_of_International_Congresses_of_Mathematicians_Plenary_and_Invited_Speakers) at the [International Congress of Mathematicians](/source/International_Congress_of_Mathematicians) in [Nice](/source/Nice). In 1987 he received the [Prize Ampère](/source/Prize_Amp%C3%A8re) from the [French Academy of Sciences](/source/French_Academy_of_Sciences). In 1995 he received the [Cole Prize](/source/Cole_Prize), together with [David Harbater](/source/David_Harbater), for his solution of the [Abhyankar conjecture](/source/Abhyankar_conjecture).[3]

## Personal life

He practiced skiing (especially in [Val-d'Isère](/source/Val-d'Is%C3%A8re)), tennis, and rock climbing (in [Fontainebleau](/source/Fontainebleau)).[2] He was married to the mathematician [Michèle Raynaud](/source/Mich%C3%A8le_Raynaud) ([née](/source/Birth_name#Maiden_and_married_names) Chaumartin)[3] who also worked with [Alexander Grothendieck](/source/Alexander_Grothendieck).

## References

1. ^ [***a***](#cite_ref-SMF_1-0) [***b***](#cite_ref-SMF_1-1) [Décès de Michel Raynaud](http://smf.emath.fr/content/d%C3%A9c%C3%A8s-de-michel-raynaud). Société Mathématique de France.

1. ^ [***a***](#cite_ref-smf-obit_2-0) [***b***](#cite_ref-smf-obit_2-1) [Gassiat, Elisabeth](/source/%C3%89lisabeth_Gassiat) (March 2018). ["Décès de Michel Raynaud"](https://smf.emath.fr/actualites-smf/deces-de-michel-raynaud). *Société Mathématique de France* (in French). Retrieved 2018-03-14.

1. ^ [***a***](#cite_ref-:0_3-0) [***b***](#cite_ref-:0_3-1) [***c***](#cite_ref-:0_3-2) [***d***](#cite_ref-:0_3-3) [***e***](#cite_ref-:0_3-4) [***f***](#cite_ref-:0_3-5) [***g***](#cite_ref-:0_3-6) [Illusie, Luc](/source/Luc_Illusie) (2019). ["Michel Raynaud (1938–2018)"](https://www.ams.org/journals/notices/201901/rnoti-p37.pdf) (PDF). *[Notices of the American Mathematical Society](/source/Notices_of_the_American_Mathematical_Society)*. **66** (1). [doi](/source/Doi_(identifier)):[10.1090/noti1764](https://doi.org/10.1090%2Fnoti1764). [S2CID](/source/S2CID_(identifier)) [125558400](https://api.semanticscholar.org/CorpusID:125558400). Retrieved 18 August 2020.

1. **[^](#cite_ref-4)** Raynaud, Michel (1983). "Sous-variétés d'une variété abélienne et points de torsion". In [Artin, Michael](/source/Michael_Artin); [Tate, John](/source/John_Tate_(mathematician)) (eds.). *Arithmetic and geometry. Papers dedicated to I. R. Shafarevich on the occasion of his sixtieth birthday. Vol. I: Arithmetic*. Progress in Mathematics (in French). Vol. 35. Boston, MA: [Birkhäuser Boston](/source/Birkh%C3%A4user). pp. 327–352. [MR](/source/MR_(identifier)) [0717600](https://mathscinet.ams.org/mathscinet-getitem?mr=0717600). [Zbl](/source/Zbl_(identifier)) [0581.14031](https://zbmath.org/?format=complete&q=an:0581.14031).

1. **[^](#cite_ref-5)** Raynaud, Michel (1985). "Hauteurs et isogénies" [Heights and isogenies]. In Szpiro, Lucien (ed.). *Séminaire sur les pinceaux arithmétiques: la conjecture de Mordell* [*Seminar on arithmetic pencils: the Mordell conjecture*]. [Astérisque](/source/Ast%C3%A9risque) (in French). Paris: Société Mathématique de France. pp. 199–234. [ISSN](/source/ISSN_(identifier)) [0303-1179](https://search.worldcat.org/issn/0303-1179). [MR](/source/MR_(identifier)) [0801923](https://mathscinet.ams.org/mathscinet-getitem?mr=0801923). [Zbl](/source/Zbl_(identifier)) [1182.14049](https://zbmath.org/?format=complete&q=an:1182.14049).

1. **[^](#cite_ref-6)** Raynaud, Michel (1994). "Revêtements de la droite affine en caractéristique p > 0". *Inventiones Mathematicae*. **116** (1): 425–462. [Bibcode](/source/Bibcode_(identifier)):[1994InMat.116..425R](https://ui.adsabs.harvard.edu/abs/1994InMat.116..425R). [doi](/source/Doi_(identifier)):[10.1007/BF01231568](https://doi.org/10.1007%2FBF01231568). [S2CID](/source/S2CID_(identifier)) [122286118](https://api.semanticscholar.org/CorpusID:122286118). [Zbl](/source/Zbl_(identifier)) [0798.14013](https://zbmath.org/?format=complete&q=an:0798.14013)..

1. **[^](#cite_ref-7)** Harbater, David (1994). "Abhyankar's conjecture on Galois groups over curves". *Inventiones Mathematicae*. **117** (1): 1–25. [Bibcode](/source/Bibcode_(identifier)):[1994InMat.117....1H](https://ui.adsabs.harvard.edu/abs/1994InMat.117....1H). [doi](/source/Doi_(identifier)):[10.1007/BF01232232](https://doi.org/10.1007%2FBF01232232). [S2CID](/source/S2CID_(identifier)) [121690794](https://api.semanticscholar.org/CorpusID:121690794). [Zbl](/source/Zbl_(identifier)) [0805.14014](https://zbmath.org/?format=complete&q=an:0805.14014)..

1. **[^](#cite_ref-FJ70_8-0)** [Fried, Michael D.](/source/Michael_D._Fried); [Jarden, Moshe](/source/Moshe_Jarden) (2008). *Field arithmetic*. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. Vol. 11 (3rd ed.). [Springer-Verlag](/source/Springer-Verlag). p. 70. [ISBN](/source/ISBN_(identifier)) [978-3-540-77269-9](https://en.wikipedia.org/wiki/Special:BookSources/978-3-540-77269-9). [Zbl](/source/Zbl_(identifier)) [1145.12001](https://zbmath.org/?format=complete&q=an:1145.12001).

1. **[^](#cite_ref-9)** Lang, William E. (1979). ["Quasi-elliptic surfaces in characteristic three"](http://www.numdam.org/item?id=ASENS_1979_4_12_4_473_0). *[Annales Scientifiques de l'École Normale Supérieure](/source/Annales_Scientifiques_de_l'%C3%89cole_Normale_Sup%C3%A9rieure)*. Série 4. **12** (4): 473–500. [doi](/source/Doi_(identifier)):[10.24033/asens.1373](https://doi.org/10.24033%2Fasens.1373). [ISSN](/source/ISSN_(identifier)) [0012-9593](https://search.worldcat.org/issn/0012-9593). [MR](/source/MR_(identifier)) [0565468](https://mathscinet.ams.org/mathscinet-getitem?mr=0565468).

1. **[^](#cite_ref-10)** Lang, William E. (1983). "Examples of surfaces of general type with vector fields". *Arithmetic and geometry, Vol. II*. Progress in Mathematics. Vol. 36. Boston, MA: Birkhäuser Boston. pp. 167–173. [MR](/source/MR_(identifier)) [0717611](https://mathscinet.ams.org/mathscinet-getitem?mr=0717611).

## External links

- [Michel Raynaud](https://mathgenealogy.org/id.php?id=77935) at the [Mathematics Genealogy Project](/source/Mathematics_Genealogy_Project)

- [Cole Prize citation for Michel Raynaud](https://www.ams.org/notices/199504/prize-cole.pdf)

- [Illusie, Luc](/source/Luc_Illusie) (January 2019). ["Michel Raynaud (1938–2018)"](https://www.ams.org/publications/journals/notices/201901/rnoti-p37.pdf) (PDF). *[Notices of the American Mathematical Society](/source/Notices_of_the_American_Mathematical_Society)*. **66** (1): 37–41. [doi](/source/Doi_(identifier)):[10.1090/noti1764](https://doi.org/10.1090%2Fnoti1764).

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Adapted from the Wikipedia article [Michel Raynaud](https://en.wikipedia.org/wiki/Michel_Raynaud) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Michel_Raynaud?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.