thumb {{Short description|French mathematician (1924–1987)}} '''Michel Paul Lazard''' (5 December 1924 – 15 September 1987) was a French mathematician who worked on the theory of Lie groups in the context of {{nowrap|''p''-adic}} analysis.
== Career and research == Born in Paris, Lazard studied at the University of Paris–Sorbonne, where he obtained his Ph.D. in 1954 under the direction of Albert Châtelet, with thesis titled ''Sur les groupes nilpotents et les anneaux de Lie''.<ref>{{MathGenealogy|id=251730}}</ref> Subsequently he was a professor at the University of Poitiers and the University of Paris 7. He died of suicide at the age of 63.
His work took on a life of its own in the hands of Daniel Quillen in the late 20th century. Quillen's discovery, that a ring Lazard used to classify formal group laws was isomorphic to an important ring in topology, led to the subject of chromatic homotopy theory. Lazard's self-contained treatise on one-dimensional formal groups also gave rise to the field of ''p''-divisible groups. His major contributions were: * The classification of ''p''-adic Lie groups: every ''p''-adic Lie group is a closed subgroup of <math>{\rm GL}_n(\mathbb{Z}_p)</math>. * The classification of (1-dimensional commutative) formal groups. * The universal formal group law coefficient ring (Lazard's universal ring) is a polynomial ring. * The concept of "analyseurs", reinvented by J. Peter May under the name operads.
== Awards and honours == In 1958, Lazard was the first recipient of the ''Prix Audin'', named after the young French mathematician Maurice Audin, who had been assassinated in Algeria.{{efn|Audin's Ph.D. dissertation was approved posthumously in December 1957 by Laurent Schwartz and Jacques Dixmier.}}<ref>{{cite web|url= https://www.association-audin.fr/presentation/|work=association-audin.fr|title=Association Audin|date=19 November 2020 |access-date=11 June 2022|language=fr}}</ref><ref>{{cite web|url=https://mathshistory.st-andrews.ac.uk/Extras/Audin_thesis/|title=Commemoration of Michel Audin's thesis|publisher=University of St Andrews|date=January 2019|access-date=11 June 2022}}</ref> In 1972, he was awarded the Prix Poncelet by the Académie des Sciences for his work on algebra.<ref>{{cite journal|journal=Comptes Rendus de l'Académie des Sciences, Série A et B|volume=275| date=11 December 1972| pages=133–134| title=Vie Académique: prix et subventions attribuées en 1972|url= https://gallica.bnf.fr/ark:/12148/bpt6k5619450s/f24.item}}</ref>
==Notes== {{notelist}} {{reflist}}
==References== *{{Citation | last=Adams | first=J. Frank |author-link=J. Frank Adams| title=Stable homotopy and generalised homology | url=https://books.google.com/books?id=6vG13YQcPnYC | publisher=University of Chicago Press |series=Chicago Lectures in Mathematics| isbn=978-0-226-00524-9 | year=1974|mr=0402720}} *{{cite book|mr=2124841 |last=Chevalley|first= Claude| author-link= Claude Chevalley |language=fr|title=Classification des groupes algébriques semi-simples [The classification of semisimple algebraic groups, with the collaboration of P. Cartier, A. Grothendieck and M. Lazard]|series=Collected works|volume=3|publisher= Springer-Verlag|year= 2005|isbn= 3-540-23031-9}} New edition of ''Séminaire C. Chevalley'', 1956–1958: Classification des groupes de Lie algébriques, Secrétariat Math., 11 rue Pierre Curie, Paris, 1958. *{{Cite journal |last=Lazard |first=Michel |year=1954 |title=Sur les groupes nilpotents et les anneaux de Lie |url=http://www.numdam.org/item?id=ASENS_1954_3_71_2_101_0 |journal=Annales Scientifiques de l'École Normale Supérieure |volume=71 |issue=2 |pages=101–190 |language=fr|doi=10.24033/asens.1021 | doi-access=free|mr=0088496|url-access=subscription }} *{{Citation | last=Lazard | first=Michel | title=Sur les groupes de Lie formels à un paramètre | url=http://www.numdam.org/item?id=BSMF_1955__83__251_0 | mr=0073925 | year=1955 | journal=Bulletin de la Société Mathématique de France | issn=0037-9484 | volume=83 | pages=251–274| language=fr| doi=10.24033/bsmf.1462 | doi-access=free | url-access=subscription }} * {{cite journal | mr = 0209286|last=Lazard |first= Michel| title= Groupes analytiques p-adiques| language=fr| journal= Publications Mathématiques de l'IHÉS |volume=26| year =1965| pages= 389–603|zbl=0139.02302|url=http://www.numdam.org/item/PMIHES_1965__26__5_0/}} *{{Citation | last=Lazard | first=Michel | title=Commutative Formal Groups | publisher=Springer-Verlag | location=Berlin, New York | series=Lecture Notes in Mathematics | isbn=978-3-540-07145-7 | doi=10.1007/BFb0070554 | mr=0393050 | year=1975 | volume=443}} *{{citation |mr=0253350| author-link=Daniel Quillen| last= Quillen|first= Daniel |title=On the formal group laws of unoriented and complex cobordism theory|journal= Bulletin of the American Mathematical Society |volume=75 | issue=6|year=1969 |pages=1293–1298 |doi=10.1090/S0002-9904-1969-12401-8 |doi-access=free }} *{{Citation | last=Serre | first=Jean-Pierre | author-link=Jean-Pierre Serre | title=Séminaire Bourbaki | publisher=Société Mathématique de France | location=Paris | mr=0176987 |zbl=0163.02901 | year=1964 | volume=8 | chapter= Groupes analytiques p-adiques (d'après Michel Lazard), Exp. 270 | chapter-url= http://www.numdam.org/item?id=SB_1962-1964__8__401_0| pages=401–440}}
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{{DEFAULTSORT:Lazard, Michel}} Category:1924 births Category:1985 deaths Category:20th-century French mathematicians Category:Group theorists Category:Scientists from Paris Category:University of Paris alumni Category:Academic staff of the University of Poitiers Category:Academic staff of the University of Paris