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:
“Social and scientific progress are assured, sir, once our great system of postpossession payments is in operation, not the installment plan, no sir, but a system of small postpossession payments that clinch the investment. No possible rational human wish unfulfilled. A man with a salary of fifty dollars a week can start payments on a Rolls-Royce, the Waldorf-Astoria, or a troupe of trained seals if he so desires.”
—John Dos Passos (1896–1970)
“Mankind is not a circle with a single center but an ellipse with two focal points of which facts are one and ideas the other.”
—Victor Hugo (1802–1885)
“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)