# 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. 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.

## 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

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