Rational Point - Rational Points of Schemes

Rational Points of Schemes

In the parlance of morphisms of schemes, a K-rational point of a scheme X is just a morphism Spec KX. The set of K-rational points is usually denoted X(K).

If a scheme or variety X is defined over a field k, a point xX is also called a rational point if its residue field k(x) is isomorphic to k.

See also: functor of points.

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Famous quotes containing the words rational, points and/or schemes:

    Since the Greeks, Western man has believed that Being, all Being, is intelligible, that there is a reason for everything ... and that the cosmos is, finally, intelligible. The Oriental, on the other hand, has accepted his existence within a universe that would appear to be meaningless, to the rational Western mind, and has lived with this meaninglessness. Hence the artistic form that seems natural to the Oriental is one that is just as formless or formal, as irrational, as life itself.
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