Density of rational points on diagonal quartic surfaces

Details Density of rational points on diagonal quartic surfaces Density of rational points on diagonal quartic surfaces

2008-12-27

arxiv.org/abs/0812.4779v3

Mathematics

Algebraic Geometry

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Scientific paper

Let a,b,c,d be nonzero rational numbers whose product is a square, and let V
be the diagonal quartic surface in PP^3 defined by ax^4+by^4+cz^4+dw^4=0. We
prove that if V contains a rational point that does not lie on any of the 48
lines on V or on any of the coordinate planes, then the set of rational points
on V is dense in both the Zariski topology and the real analytic topology.

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