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Simultaneous twists of elliptic curves and the Hasse principle for certain K3 surfaces
2017
In this thesis we unconditionally show that certain K3 surfaces satisfy the Hasse principle. Our method involves the 2-Selmer groups of simultaneous quadratic twists of two elliptic curves, only with places of good or additive reduction. More generally we prove that, given finitely many such elliptic curves defined over a number field (with rational 2-torsion and satisfying some mild conditions) there exists an explicit quadratic extension such that the quadratic twist of each elliptic curve
doi:10.7916/d81c1wvg
fatcat:prox6fsdcjaizgda45mlof6254