Rational Points of Schemes
In the parlance of morphisms of schemes, a K-rational point of a scheme X is just a morphism Spec K→X. 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 x∈X is also called a rational point if its residue field k(x) is isomorphic to k.
See also: functor of points.
Read more about this topic: Rational Point
Famous quotes containing the words rational, points and/or schemes:
“... the happiness of a people is the only rational object of government, and the only object for which a people, free to choose, can have a government at all.”
—Frances Wright (1795–1852)
“We only part to meet again.
Change, as ye list, ye winds: my heart shall be
The faithful compass that still points to thee.”
—John Gay (1685–1732)
“Science is a dynamic undertaking directed to lowering the degree of the empiricism involved in solving problems; or, if you prefer, science is a process of fabricating a web of interconnected concepts and conceptual schemes arising from experiments and observations and fruitful of further experiments and observations.”
—James Conant (1893–1978)