Rational point

From Wikipedia, the free encyclopedia

In number theory, a K-rational point is a point on an algebraic variety where each coordinate of the point belongs to the field K.

Rational points of varieties constitute a major area of current research. In general, it's possible and useful to put a group structure over the rational points.

The Mordell-Weil theorem states that the group of rational points of a variety over K is finitely generated if K is a number field. The Weil conjectures concern the varietes over finite fields.