Glossary of algebraic geometry
Глоссарий алгебраической геометрии
代数幾何学用語一覧
Глосарій алгебричної геометрії
代数幾何学用語一覧（だいすうきかがくようごいちらん、英: glossary of algebraic geometry）では、代数幾何学で使われる用語を一覧にまとめる。 、、も参照。数論的な応用については参照。 この記事では、簡単のために基底スキームについての明記をしばしば省略する。つまり、ある基底スキーム S 上のスキームのことを単にスキームと言ったり S 射のことを射と言ったりする。
This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory. For the number-theoretic applications, see glossary of arithmetic and Diophantine geometry. For simplicity, a reference to the base scheme is often omitted; i.e., a scheme will be a scheme over some fixed base scheme S and a morphism an S-morphism.
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Algebraic geometry occupied a central place in the mathematics of the last century. The deepest results of Abel, Riemann, Weierstrass, many of the most important papers of Klein and Poincare belong to this domain. At the end of the last and the beginning of the present century the attitude towards algebraic geometry changed abruptly. ... The style of thinking that was fully developed in algebraic geometry at that time was too far removed from the set-theoretical and axiomatic spirit, which then determined the development of mathematics. ... Around the middle of the present century algebraic geometry had undergone to a large extent such a reshaping process. As a result, it can again lay claim to the position it once occupied in mathematics.
On Grothendieck's own view there should be almost no history of schemes, but only a history of the resistance to them: ... There is no serious historical question of how Grothendieck found his definition of schemes. It was in the air. Serre has well said that no one invented schemes . The question is, what made Grothendieck believe he should use this definition to simplify an 80 page paper by Serre into some 1000 pages of Éléments de géométrie algébrique?
From the preface to I.R. Shafarevich, Basic Algebraic Geometry.
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This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory. For the number-theoretic applications, see glossary of arithmetic and Diophantine geometry. For simplicity, a reference to the base scheme is often omitted; i.e., a scheme will be a scheme over some fixed base scheme S and a morphism an S-morphism.
代数幾何学用語一覧（だいすうきかがくようごいちらん、英: glossary of algebraic geometry）では、代数幾何学で使われる用語を一覧にまとめる。 、、も参照。数論的な応用については参照。 この記事では、簡単のために基底スキームについての明記をしばしば省略する。つまり、ある基底スキーム S 上のスキームのことを単にスキームと言ったり S 射のことを射と言ったりする。
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