Michel Lazard

Michel Paul Lazard (5 December 1924 – 23 December 1985) 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, lead to the subject of chromatic homotopy theory.

Lazard's self contained treatise on one-dimensional formal groups also birthed the field of p-divisible groups.

His major contributions:

• classification of p-adic Lie groups: every p-adic Lie group is a closed subgroup of $GL_n(\mathbb{Z}_p)$
• 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 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, 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: 1293–1298, doi:10.1090/S0002-9904-1969-12401-8, MR 0253350