| 词条 | Radicial morphism |
| 释义 |
In algebraic geometry, a morphism of schemes f: X → Y is called radicial or universally injective, if, for every field K the induced map X(K) → Y(K) is injective. (EGA I, (3.5.4)) This is a generalization of the notion of a purely inseparable extension of fields (sometimes called a radicial extension, which should not be confused with a radical extension.) It suffices to check this for K algebraically closed. This is equivalent to the following condition: f is injective on the topological spaces and for every point x in X, the extension of the residue fields k(f(x)) ⊂ k(x) is radicial, i.e. purely inseparable. It is also equivalent to every base change of f being injective on the underlying topological spaces. (Thus the term universally injective.) Radicial morphisms are stable under composition, products and base change. If gf is radicial, so is f. References
1 : Morphisms of schemes |
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