[過去ﾛｸﾞ] 現代数学の系譜11 ガロア理論を読む14 [転載禁止]©2ch.net (562ﾚｽ)
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516(1): 現代数学の系譜11 ガロア理論を読む [] 2015/08/09(日) 13:14:07.11 ID:+PUkznvl(27/29) AAS
>>515
でもさ、1974以降の代数幾何の大きな発展ってないのかね？
繰り返すが、グロタン先生がいなくなって、発展が止まった？
そんなことないでしょうよ
だったらさ、「普通はハーツホーンとか読む ウィキなんか知るかって態度が正解」と言えるのかね？
518: 現代数学の系譜11 ガロア理論を読む [] 2015/08/09(日) 13:25:39.71 ID:+PUkznvl(28/29) AAS
>>516 つづき
お嫌いですか、en.wikipedia
https://en.wikipedia.org/wiki/Algebraic_geometry
Algebraic geometry
ontents
略
3 Computational algebraic geometry
3.1 Grobner basis
3.2 Cylindrical Algebraic Decomposition (CAD)
3.3 Asymptotic complexity vs. practical efficiency
4 Abstract modern viewpoint
5 History
5.1 Prehistory: before the 16th century
5.2 Renaissance
5.3 19th and early 20th century
5.4 20th century
6 Analytic geometry
7 Applications
8 See also
9 Notes
10 Further reading
11 External links
History 20th century 1970以降抜粋
After a decade of rapid development the field stabilized in the 1970s, and new applications were made, both to number theory and to more classical geometric questions on algebraic varieties, singularities and moduli.
An important class of varieties, not easily understood directly from their defining equations, are the abelian varieties, which are the projective varieties whose points form an abelian group.
The prototypical examples are the elliptic curves, which have a rich theory. They were instrumental in the proof of Fermat's last theorem and are also used in elliptic curve cryptography.
In parallel with the abstract trend of the algebraic geometry, which is concerned with general statements about varieties,
methods for effective computation with concretely-given varieties have also been developed, which lead to the new area of computational algebraic geometry.
One of the founding methods of this area is the theory of Grobner bases, introduced by Bruno Buchberger in 1965.
Another founding method, more specially devoted to real algebraic geometry, is the cylindrical algebraic decomposition, introduced by George E. Collins in 1973.
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