現代数学の系譜古典ガロア理論を読む37

現代数学の系譜古典ガロア理論を読む37at MATH

現代数学の系譜古典ガロア理論を読む37 - 暇つぶし2ch579: 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. つづく

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