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11(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP [sage] 2020/06/21(日) 08:08:24.19 ID:W0WIc7wX(5/18) AAS
>>10
つづき
・ザリスキの主定理：
https://ja.wikipedia.org/wiki/%E3%82%AA%E3%82%B9%E3%82%AB%E3%83%BC%E3%83%BB%E3%82%B6%E3%83%AA%E3%82%B9%E3%82%AD
オスカー・ザリスキ
主な業績は、ザリスキ位相の導入やザリスキの主定理（英語版）の証明を含む可換環論と代数幾何の融合である。
弟子に、ダニエル・ゴーレンシュタイン、広中平祐、ミハイル・アルティン、デヴィッド・マンフォード、ロビン・ハーツホーンら著名な数学者がたくさんおり、優れた指導者でもあった。
https://en.wikipedia.org/wiki/Zariski%27s_main_theorem
Zariski's main theorem
In algebraic geometry, Zariski's main theorem, proved by Oscar Zariski (1943), is a statement about the structure of birational morphisms stating roughly that there is only one branch at any normal point of a variety. It is the special case of Zariski's connectedness theorem when the two varieties are birational.
Zariski's main theorem can be stated in several ways which at first sight seem to be quite different, but are in fact deeply related. Some of the variations that have been called Zariski's main theorem are as follows:
略
The name "Zariski's main theorem" comes from the fact that Zariski labelled it as the "MAIN THEOREM" in Zariski (1943).
略
つづく
12(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP [sage] 2020/06/21(日) 08:09:07.81 ID:W0WIc7wX(6/18) AAS
>>11
つづき
・チェボタレフの密度定理：
https://en.wikipedia.org/wiki/Chebotarev%27s_density_theorem
Chebotarev's density theorem
Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field {\displaystyle \mathbb {Q} of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic integers of K. There are only finitely many patterns of splitting that may occur. Although the full description of the splitting of every prime p in a general Galois extension is a major unsolved problem, the Chebotarev density theorem says that the frequency of the occurrence of a given pattern, for all primes p less than a large integer N, tends to a certain limit as N goes to infinity. It was proved by Nikolai Chebotaryov in his thesis in 1922, published in (Tschebotareff 1926).
Contents
1 History and motivation
2 Relation with Dirichlet's theorem
3 Formulation
4 Statement
4.1 Effective Version
4.2 Infinite extensions
5 Important consequences
つづく
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