Integer points on homogeneous varieties with two or more degrees

Abstract

We give a revised version of Schmidt's treatment of forms in many variables, which allows us to prove a Hasse principle under more lenient conditions on the number of variables than what had previously been thought possible with these methods. Our results are generally comparable with recent advances in the field and supersede them in a number of cases.

Withdrawn due to a crucial error on page 8. Thanks to D.R. Heath-Brown for spotting this