@article{228, abstract = {Let X be a projective non-singular quartic hypersurface of dimension 39 or more, which is defined over . We show that X() is non-empty provided that X() is non-empty and X has p-adic points for every prime p.}, author = {Timothy Browning and Heath-Brown, Roger}, journal = {Journal fur die Reine und Angewandte Mathematik}, number = {629}, pages = {37 -- 88}, publisher = {Walter de Gruyter}, title = {{Rational points on quartic hypersurfaces}}, doi = {10.1515/CRELLE.2009.026}, year = {2009}, }