Rational points on cubic hypersurfaces over ${\mathbb{F}}_q(t)$

Abstract

For any finite field k of characteristic exceeding 3, the Hasse principle and weak approximation is established for non-singular cubic hypersurfaces X over the function field k(t), provided that X has dimension at least 6.

64 pages; minor changes to the Introduction, Section 3 and Remark 8.6