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. 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 are:
- The classification of p-adic Lie groups: every p-adic Lie group is a closed subgroup of .
- 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.
- 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