Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces

Details Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces

2007-08-21

arxiv.org/abs/0708.2752v1

Mathematics

Number Theory

17 pages, comments welcome

Scientific paper

We show that if over some number field there exists a certain diagonal plane
cubic curve that is locally solvable everywhere, but that does not have points
over any cubic galois extension of the number field, then the algebraic part of
the Brauer-Manin obstruction is not the only obstruction to the Hasse principle
for K3 surfaces.

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