We establish an analytic Hasse principle for linear spaces of affine dimension on a complete intersection over an algebraic field extension of . The number of variables required to do this is no larger than what is known for the analogous problem over . As an application, we show that any smooth hypersurface over whose dimension is large enough in terms of the degree is -unirational, provided that either the degree is odd or is totally imaginary.
"Linear Spaces on Hypersurfaces over Number Fields." Michigan Math. J. 66 (4) 769 - 784, November 2017. https://doi.org/10.1307/mmj/1501207390