Jean-Louis Verdier

Jean-Louis Verdier (1935 – 1989) was a French mathematician who worked, under the guidance of Alexander Grothendieck, on derived categories and Verdier duality. He was a close collaborator of Alexander Grothendieck, notably contributing to SGA 4 his theory of hypercovers and anticipating the later development of étale homotopy by Michael Artin 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 etale topological type.

In 1976 he developed a useful regularity condition on stratified sets that T.-C. Kuo had previously shown was stronger than the Whitney conditions for subanalytic sets (like analytic varieties). Verdier called the condition (w) for Whitney, as at the time he thought (w) might be equivalent to Whitney's condition (b). Semi-algebraic and then real algebraic counterexamples were constructed by David Trotman who has since studied many geometric properties of (w)-regular stratifications.

Verdier later worked on the theory of integrable systems.

References

*
* Verdier's 1967 thesis, published belatedly in:
*:cite journal
last = Verdier
first = Jean-Louis
title = Des Catégories Dérivées des Catégories Abéliennes
journal = Astérisque
volume = 239
publisher = Société Mathématique de France, Marseilles
date = 1996
language = French:Part of it also appears in SGA 4 1/2 as the last chapter, "Catégories dérivées (état 0)".
* J.-L. Verdier, "Stratifications de Whitney et théorème de Bertini-Sard", Inventiones Math. 36 (1976), 295-312
*"The Verdier Memorial Conference on Integrable Systems: Actes du Colloque International de Luminy" (1991) (Progress in Mathematics) edited by V. Babelon, P. Cartier, Y. Kosmann-Schwarzbach