Michel Lazard

Michel Paul Lazard (5 December 1924 – 15 September 1987) was a French mathematician who worked in the theory of Lie groups in the context of p-adic analysis.

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".^[1] Subsequently he was a Professor at the University of Poitiers and the University of Paris 7.

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 ${\displaystyle {\rm {GL}}_{n}(\mathbb {Z} _{p})}$.
• 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.

References[]

• Adams, J. Frank (1974), Stable homotopy and generalised homology, University of Chicago Press, ISBN 978-0-226-00524-9
• Lazard, Michel (1955), "Sur les groupes de Lie formels à un paramètre", Bulletin de la Société Mathématique de France, 83: 251–274, doi:10.24033/bsmf.1462, ISSN 0037-9484, MR 0073925
• Lazard, Michel (1975), Commutative formal groups, Lecture Notes in Mathematics, 443, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0070554, ISBN 978-3-540-07145-7, MR 0393050
• Quillen, Daniel (1969), "On the formal group laws of unoriented and complex cobordism theory", Bulletin of the American Mathematical Society, 75 (6): 1293–1298, doi:10.1090/S0002-9904-1969-12401-8, MR 0253350
• Serre, Jean-Pierre (1964), "Groupes analytiques p-adiques (d'après Michel Lazard), Exp. 270", Séminaire Bourbaki, 8, Paris: Société Mathématique de France, pp. 401–440, MR 0176987, Zbl 0163.02901

Notes[]