W be a regular map. Prove that ¢ is constant. 30 A. 2. Let X and Y be projective varieties defined over a field k. (a) If X(k) 1= 0 and there is a k-morphism f : X -+ Y, prove that Y(k) 1= 0. (b) If X and Y are k-birationally equivalent, prove that X(k) is dense in X (for the Zariski topology) if and only if Y(k) is dense in Y.
Diophantine Geometry: An Introduction by Marc Hindry
by Steven
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