Jean-Louis Verdier (; 2 February 1935 – 25 August 1989) was a
French
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mathematician
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Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
SGA 4 SGA may refer to:
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Michael Artin
Michael Artin (; born 28 June 1934) is a German-American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry.Barry Mazur, following a suggestion he attributed to Pierre Cartier. Saul Lubkin's related theory of rigid hypercovers was later taken up by
Eric Friedlander
Eric Mark Friedlander (born January 7, 1944 in Santurce, Puerto Rico) is an American mathematician who is working in algebraic topology, algebraic geometry, algebraic K-theory and representation theory.
Friedlander graduated from Swarthmor ...
École Normale Supérieure
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in Paris, and later became director of studies there, as well as a Professor at the University of Paris VII. For many years he directed a joint seminar at the École Normale Supérieure with Adrien Douady. Verdier was a member of Bourbaki. In 1984 he was the president of the Société Mathématique de France.
In 1976 Verdier developed a useful regularity condition on stratified sets that the Chinese-Australian mathematician Tzee-Char Kuo had previously shown implied the Whitney conditions for
subanalytic set In mathematics, particularly in the subfield of real analytic geometry, a subanalytic set is a set of points (for example in Euclidean space) defined in a way broader than for semianalytic sets (roughly speaking, those satisfying conditions requir ...
s (such as real or complex analytic varieties). Verdier called the condition (w) for Whitney, as at the time he thought (w) might be equivalent to Whitney's condition (b). Real algebraic examples for which the Whitney conditions (b) hold but Verdier's condition (w) fails, were constructed by David Trotman who has obtained many geometric properties of (w)-regular stratifications. Work of Bernard Teissier, aided by Jean-Pierre Henry and Michel Merle at the École Polytechnique, led to the 1982 result that Verdier's condition (w) is equivalent to the Whitney conditions for complex analytic stratifications.
Verdier later worked on the theory of
integrable system
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first ...
Yvette Kosmann-Schwarzbach
Yvette Kosmann-Schwarzbach (born 30 April 1941) is a French mathematician and professor. She has been teaching mathematics at the Lille University of Science and Technology and at the École polytechnique since 1993. Kosmann-Schwarzbach obtained ...
: ''Integrable systems. The Verdier memorial colloquium.'' Birkhäuser, Progress in Mathematics, 1993.
Bibliography
* Verdier's 1967 thesis, published belatedly in:
*:
:Part of it also appears in SGA 4½ as the last chapter, "Catégories dérivées (état 0)".
*
''Integrable Systems, The Verdier Memorial Conference'' (Actes du Colloque International de Luminy, 1991), Progress in Mathematics 115, edited by O. Babelon, P. Cartier, Y. Kosmann-Schwarzbach, Birkhäuser, 1993.
See also
*
Artin–Verdier duality
In mathematics, Artin–Verdier duality is a duality theorem for constructible abelian sheaves over the spectrum of a ring of algebraic numbers, introduced by , that generalizes Tate duality.
It shows that, as far as etale (or flat) cohomol ...