论文标题
代数等同于通勤领域
Algebraic equivarieties over a commutative field
论文作者
论文摘要
由于使用规范和$*$*$*$*$*$*$*$*$*$*$*$*$*$*$*$*，我们将先前创立的等效代数几何形状的基本理论扩展到任意交换领域的基本理论，并将其在通勤领域的（等值词）代数的（等效性）代数的理论扩展到了仿期代数几何的概括（通过规范代数几何）的概括。我们在这里以等效且更具启发性的“具体”设置为基础场中的结构或骨带有结构性或骨，这使我们能够对一般的eprivarieties的产物进行固定的理论描述。与代数封闭的特定情况一样，局部封闭的亚各种自然配备了均衡结构，这尤其允许将所有准标记（Equi）品种融合到代数（Equi）品种类别中。
We expand our previously founded basic theory of equiresidual algebraic geometry over an arbitrary commutative field, to a well-behaved theory of (equiresidual) algebraic varieties over a commutative field, thanks to the generalisation of affine algebraic geometry by the use of canonical localisations and $*$-algebras. We work here in an equivalent and more suggestive "concrete" setting with structural sheaves of functions into the base field, which allows us to give a set-theoretic description of the products of equivarieties in general. Locally closed subvarieties are naturally equipped with an equivariety structure as in the particular case of algebraically closed fields, and this allows in particular to embed all quasi-projective (equi)varieties in general into the category of algebraic (equi)varieties.
