Jean-Louis Verdier (; 2 February 1935 – 25 August 1989) was a
French mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
who worked, under the guidance of his doctoral advisor
Alexander Grothendieck
Alexander Grothendieck, later Alexandre Grothendieck in French (; ; ; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research ext ...
, on
derived categories and
Verdier duality. He was a close collaborator of Grothendieck, notably contributing to
SGA 4 his theory of
hypercovers and anticipating the later development of
étale homotopy by
Michael Artin
Michael Artin (; born 28 June 1934) is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology Mathematics Department, known for his contributions to algebraic geometry. and
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 in his definition of the
étale topological type.
Verdier was a student at the elite
École Normale Supérieure
École or Ecole may refer to:
* an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing i ...
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
Adrien Douady (; 25 September 1935 – 2 November 2006) was a French mathematician born in La Tronche, Isère. He was the son of Daniel Douady and Guilhen Douady.
Douady was a student of Henri Cartan at the École normale supérieure, and initi ...
. 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 In differential topology, a branch of mathematics, the Whitney conditions are conditions on a pair of submanifolds of a manifold introduced by Hassler Whitney in 1965.
A stratification of a topological space is a finite filtration by closed subsets ...
for
subanalytic sets (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
(, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris.
The school was founded in 1794 by mat ...
, 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 systems.
[Olivier Babelon, Pierre Cartier, Yvette Kosmann-Schwarzbach: ''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
References
External links
*
{{DEFAULTSORT:Verdier, Jean-Louis
1935 births
1989 deaths
École Normale Supérieure alumni
20th-century French mathematicians
University of Paris alumni
Academic staff of the University of Paris
Nicolas Bourbaki