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.
Read more about this topic: Imaginary Point
Famous quotes containing the words rational, points and/or schemes:
“It is not to be forgotten that what we call rational grounds for our beliefs are often extremely irrational attempts to justify our instincts.”
—Thomas Henry Huxley (1825–95)
“PLAIN SUPERFICIALITY is the character of a speech, in which any two points being taken, the speaker is found to lie wholly with regard to those two points.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“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)