Finite Morphisms to Projective Space and Capacity Theory

29 pages, à paraître dans: Journal für die reine und angewandte Mathematik DOI: 10.1515/crelle-2014-0089Version électronique disponible sur www.degruyter.comInternational audienceWe study conditions on a commutative ring R which are equivalent to the following requirement; whenever X is a projective scheme over S = Spec(R) of fiber dimension \leq d for some integer d \geq 0, there is a finite morphism from X to P^d_S over S such that the pullbacks of coordinate hyperplanes give prescribed subschemes of X provided these subschemes satisfy certain natural conditions. We use our results to define a new kind of capacity for subsets of the archimedean points of projective flat schemes X over the ring of integers of a number field. This capacity can be used to generalize the converse part of the Fekete-Szeg\H{o} Theorem