Radicial morphism

Radicial morphism

In algebraic geometry, a domain in mathematics, a morphism of schemes
f:XY
is called radicial or universally injective, if, for every g: Y' Y the pullback of f along g is injective.

This is equivalent to the following condition: for every point x in X, the extension of the residue fields

k(f(x)) ⊂ k(x)
is radicial, i.e. purely inseparable.

References

  • , section I.3.5.
  • , see section V.5.
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