On the degree of integral points of a projective space, by Reinie Erne

This work has now appeared in Crelle (J. reine angew. Math. 532 (2001), 151--177) and so the preprint has been removed. In this paper we suppose given a locally free module F of finite rank over the ring of integers of a number field, endowed with a Hermitian metric, and a horizontal hypersurface in the associated projective space. We show that the complement of this hypersurface contains an integral point whose degree can be bounded by an explicit(ely given) function of the degree and absolute discriminant of the field, the arithmetic degree and first successive minimum of the Hermitian vector bundle F, and the degree, dimension, and projective height of the hypersurface.

Reinie Erne <erne@univ-rennes1.fr>