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Results tagged with schemes
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user 123448
The first purpose of schemes theory is the geometrical study of solutions of algebraic systems of equations, not only over the real/complex numbers, but also over integer numbers (and more generally over any commutative ring with 1). It was finalized by Alexandre Grothendieck, during the 1950s and the 1960s.
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What algebraic condition corresponds to injectivity of a morphism of varieties?
$\DeclareMathOperator{\Spec}{Spec}$
Let $X = \Spec A$, $Y = \Spec B$ be affine complex varieties, that is reduced $\mathbb{C}$-schemes of finite type. … There should be a ring-theoretic condition on $\phi \in \operatorname{Hom}_\mathbb{C}(B, A) \cong \operatorname{Hom}_\mathsf{Sch}(X, Y)$ detecting whether the corresponding morphism of schemes is injective …
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