History of sheaf theory. (Histoire de la théorie des faisceaux.) (French) Zbl 1044.01532
Material on the history of mathematics in the 20th century. Proceedings of the colloquium to the memory of Jean Dieudonné, Nice, France, January 1996. Marseille: Société Mathématique de France (ISBN 2-85629-065-5/pbk). Sémin. Congr. 3, 101-119 (1998).
Summary: Sheaf theory was introduced by Jean Leray just after the Second World War, as a continuation of his work while he was a prisoner in Austria. Leray defined cohomology groups for continuous maps, and related them to the cohomology of the source space by means of the spectral sequence he introduced for this purpose. Henri Cartan reformulated sheaf theory in his seminar and, together with Jean-Pierre Serre, gave spectacular applications to the theory of analytic spaces. Subsequently Serre extended these methods to algebraic geometry, and then Grothendieck enlarged and generalized them enormously. Finally, Sato applied Grothendieck’s methods to \(\mathcal D\)-modules, creating microlocal analysis.
For the entire collection see [Zbl 0892.00028].
For the entire collection see [Zbl 0892.00028].
MSC:
| 01A65 | Development of contemporary mathematics |
| 55-03 | History of algebraic topology |
| 35-03 | History of partial differential equations |
| 35A27 | Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs |
