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518(1): 現代数学の系譜 古典ガロア理論を読む 2017/08/08(火)22:20 ID:dwNxNtRp(17/27) AAS
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外部ﾘﾝｸ[pdf]:www.ams.org
Cartan and Complex
Analytic Geometry

NOTICES OF THE AMS VOLUME 57, NUMBER 8 SEPTEMBER 2010
(抜粋)
Jean-Pierre Demailly
On the Mathematical Heritage of Henri Cartan
(抜粋)
Henri Cartan left us on August 13, 2008, at the age of 104.
His influence on generations of mathematicians worldwide has been considerable.
In France especially, his role as a professor at Ecole Normale Superieure in Paris between 1940 and 1965 led him to supervise the Ph.D. theses of Jean-Pierre
Serre (Fields Medal 1954), Rene Thom (Fields Medal 1958), and many other prominent mathematicians such as Pierre Cartier, Jean Cerf, Adrien Douady, Roger Godement, Max Karoubi, and Jean-Louis Koszul.
(略)
Two years later I started a Ph.D. thesis under the supervision of Henri Skoda in Paris, and it is only at this period that I began realizing the full extent of Cartan’s contributions to mathematics, in particular those on the theory of coherent analytic sheaves and his fundamental work in homological algebra and in algebraic topology [CE, CS1].
Taking part of its inspiration from J. Leray’s ideas and from the important work of K. Oka in Japan, the celebrated Cartan seminar [Ca2] ran from 1948 to 1964, and as an outcome of the work by its participants,
especially H. Cartan, J.-P. Serre, and A. Grothendieck, many results concerning topology and holomorphic functions of several variables received their final modern formulation.
One should mention especially the proof of the coherence of the ring of holomorphic functions OX in an arbitrary number of variables, after ideas of Oka, and the coherence of the ideal
sheaf of an analytic set proved by Cartan in 1950.
Another important result is the coherence of the sheaf of weakly holomorphic meromorphic functions, which leads to Oka’s theorem on the existence of the normalization of any complex space.

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