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:
“What is rational is actual and what is actual is rational. On this conviction the plain man like the philosopher takes his stand, and from it philosophy starts in its study of the universe of mind as well as the universe of nature.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“The men who carry their points do not need to inquire of their constituents what they should say, but are themselves the country which they represent: nowhere are its emotions or opinions so instant and so true as in them; nowhere so pure from a selfish infusion.”
—Ralph Waldo Emerson (1803–1882)
“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)