# Biographic Data/Stories about André Néron

Tomorrow, April 6, 2010, André Néron will have been dead for 25 years.

In spite of the weight of his work on abelian varieties, I've only been able to ascertain the following information:

1. His birth and death dates (born November 30, 1922)
2. In 1943 he graduated from the École Normale. He got his doctorate in 1951 and his advisor was Châtelet (though not at any particular school, just somewhere in Paris according to German Wikipedia) and his only student was Colliot-Thélène at Orsay (shared with Swinnerton-Dyer)
3. He was employed at Poitiers. It also seems that in 1953 when he was inducted into the Société Mathématique de France he was listed as being at Orsay. In years 59-60 he was at the IAS and in 1954 he was an invited speaker at the ICM in Amsterdam.

That's pretty much what I found. And all that does is hint that there's a really fantastic story in there!

What happened during the war?

How did he get back to mathematics?

Who else did he work with (not just publish papers with, MathSciNet suggests his only collaborators were Serge Lang and Pierre Samuel)?

Why so few students? Was he difficult to get along with or was it just a sign of the times?

Why did he die at age 62?

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(I just added the correct accents.) – François G. Dorais Apr 6 '10 at 1:34
Many Thanks, sir! – stankewicz Apr 6 '10 at 1:50
I think the question about why so few students is easily answered: french mathematicians had very little incentives to take students at the time (check how many students had Serre). Nonetheless, I will ask Colliot-Thélène about it. – Olivier Apr 6 '10 at 8:40
I remember reading somewhere that at that time in France, doctorates took 5-8 years; so it's not unlikely that the war had no affect on his doctoral work. – Frank Apr 6 '10 at 10:09
@Olivier: By coincidence I had been corresponding with Colliot-Thélène earlier today, and a few hours ago I sent him an email which drew his attention to this question. So you needn't ask him if you haven't already. – Pete L. Clark Apr 6 '10 at 10:33

In the Grothendieck-Serre correspondence, you can find some interesting quotes:

[GROTHENDIECK, OCTOBER 19, 1961]

"Je trouve que ce n'est pas malin de faire laïusser Néron sur lui-même: on ne sera pas plus avancé après qu'avant. Ne pourrait-on pas essayer de trouver un brave qui essaierait de comprendre un peu ce que fait Néron? Peut-être une série d'exposés sur Néron-Kodaira-Ogg-Tate, par Cartier ou quelque autre, puisque tout cela est lié et devrait être compris ensemble."

("I do not think it is very smart to let Néron talk about himself: we will be no better off afterwards than we were before. Couldn't we try to find someone coureageous enough to try to understand what Néron is doing? Maybe we could have a series of talks by Cartier or someone else, on Néron-Kodaira-Ogg-Tate, since all this is linked, and should be understood together".)

[SERRE, AUGUST 13, 1964]

"Il faudrait que tu m'expliques une fois ce que sont ces symboles locaux de Néron. Je n'ai rien compris à ce que Lang en disait - et je n'avais pas compris davantage le papier de Néron que j'ai eu une fois entre les mains. Mais quel animal ce Néron! Sous ses air patauds, il ne démontre jamais que des choses fondamentales! Dommage qu'il ne sache pas mieux les exposer."

("One of these days, you will have to explain to me what Néron's local symbols [are]. I understood nothing of what Lang said about them - and neither did I understand Néron's paper, which I once had a look at. What an animal Néron is! Underneath the clumsy airs, everything he proves is fundamental! It is a shame he doesn't know how to present his work better.")

Et cetera :)

An excellent question!

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Given the recent response about working in the language of Weil, do you think this business about "clumsy airs" refers to his not working in schemes? – stankewicz Apr 6 '10 at 14:59
I don't really know. From the surrounding paragraphs, I get the feeling that it must be more than just "not using schemes", but I can't be sure. – Wanderer Apr 6 '10 at 15:10

According to Colliot (sorry Pete, I missed your warning that you had already asked him), Néron was a very nice person. The fact that he had so few students simply reflect the fact that at the time there was no pressure on doctoral candidate to produce something significant ever: the worse that could happen was that you would get $only$ tenure. Consequently, there was no need to find something significant publishable quickly and consequently doctoral candidates would meet their advisor about once a year to get some papers signed and that was all. In that situation, the choice of an advisor is pretty much arbitrary.

Colliot-Thélène chose him because he wanted to do geometry but not something too closely affiliated with Grothendieck. According to him, Néron had at least another student, but I have already forgotten his name. This other student computed Néron models of modular curves of genus 1.

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There might be a little more information in an 1986 article published by the alumni magazine of ENS: google would only reveal that he was born in the small village of La Clayette and died of cancer aged 62.

Concerning the wartime hiatus: in february 1943 it was announced by french authorities that people born in either 1920, 1921, or 1922 were compelled to go and work in Germany (STO: Service de Travail Obligatoire). Since Néron was born in 1922, he either went to Germany or fled (some ENS students have described how they fled).

One thing for certain: Néron was "promotion 1943" at ENS, which means he entered the school then, not that he graduated in 1943. In fact Fields medalist René Thom also was from promotion 1943, and also completed his doctorate in 1951, so in that respect the dates are not unusual. The big difference is that Thom was born in 1923, and thus not subjected to STO.

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I am guessing that "doctorate" at the time for a student of ENS meant "Thèse d'État", so something closer to an habilitation today, and hence something you should get in around 8 years. – Olivier Apr 6 '10 at 8:38

It seems that Colliot-Thélène was asked this question three times: by me, by Olivier, and by Kevin Buzzard. Here is the reply that he gave to Kevin and forwarded to me:

Le patron d'André Néron était Albert Châtelet.

Néron eut un autre étudiant en thèse, Gérard Ligozat, qui après plusieurs travaux sur les courbes modulaires quitta le département de mathématiques.

André Néron parlait le langage de la géométrie algébrique de Weil à une époque où l'école de Grothendieck était devenu dominante. Les jeunes fringants allaient naturellement voir du côté des schémas.

La notion de patron et d'élève dans les années 1970 en France était souple. Après une excellente scolarité, on obtenait un poste quasi-permanent soit à l'Université soit au CNRS sans avoir publié une ligne dans une revue. Ensuite on faisait une thèse si on en avait envie. Voir son patron une fois par an était souvent suffisant.

Et le système, sur la durée, a marché aussi bien que dans notre époque de publish ou perish.

André Néron mourut d'un cancer en 1985.

Kevin explicitly gave Colliot-Thélène the option of responding in French, which seems appropriate given the subject matter.

English translation by François G. Dorais:

André Néron's advisor was Albert Châtelet.

Néron had one more thesis student, Gérard Ligozat, who left the Department of Mathematics after much work on modular curves.

André Néron spoke the language of Algebraic Geometry in the style of Weil at a time when the Grothendieck school had become dominant. The dashing youth naturally leaned toward [Grothendieck's] schemes.

The notion of advisor and student was flexible in France during the 1970's. After excellent scholarly work, one could obtain a quasi-permanent job either at the University or at the CNRS, without having published a single line in a journal. Then, if desired, one could do a thesis. Seeing one's advisor once per year was often enough.

And this system, while it lasted, worked just as well as the publish or perish [system] of our times.

André Néron died of cancer in 1985.

(I took a few very minor liberties for readability, but the translation is mostly literal.)

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Thanks, Francois. – Pete L. Clark Apr 6 '10 at 23:35
Pete, I thought some readers would appreciate a translation. I hope you don't mind the addition. – François G. Dorais Apr 6 '10 at 23:35
Heh, I logged in to post Colliot's response, but you got there first ;-) Cheers Pete. – Kevin Buzzard Apr 7 '10 at 18:26