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Article Dans Une Revue Journal für die reine und angewandte Mathematik Année : 2017

Finite Morphisms to Projective Space and Capacity Theory

Résumé

We 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.

Dates et versions

hal-00663474 , version 1 (27-01-2012)

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Ted Chinburg, Laurent Moret-Bailly, Georgios Pappas, Martin Taylor. Finite Morphisms to Projective Space and Capacity Theory. Journal für die reine und angewandte Mathematik, 2017, 727 (727), pp.69-84. ⟨10.1515/crelle-2014-0089⟩. ⟨hal-00663474⟩
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