Density of rational points on diagonal quartic surfaces
Copyright policy )Density of rational points on diagonal quartic surfaces
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.
added reference
- Leiden University Netherlands
- University of Montreal Canada
- University of Waterloo Canada
- Centre de Recherches Mathématiques
quartic surfaces, Mathematics - Number Theory, 11D25, K3 surfaces, rational points, Mathematics - Algebraic Geometry, elliptic surfaces, FOS: Mathematics, 14G05, Number Theory (math.NT), 14J28, Algebraic Geometry (math.AG), 11Dxx, 11Gxx, 14Gxx, 14Jxx
quartic surfaces, Mathematics - Number Theory, 11D25, K3 surfaces, rational points, Mathematics - Algebraic Geometry, elliptic surfaces, FOS: Mathematics, 14G05, Number Theory (math.NT), 14J28, Algebraic Geometry (math.AG), 11Dxx, 11Gxx, 14Gxx, 14Jxx
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