On a theorem of Faltings on formal functions
Algebraic Geometry
2008-10-10 v1
Abstract
In 1980, Faltings proved, by deep local algebra methods, a local result regarding formal functions which has the following global geometric fact as a consequence. Theorem: Let k be an algebraically closed field (of any characteristic). Let Y be a closed subvariety of a projective irreducible variety X defined over k. Assume that X \subseteq P^n, dim(X)=d>2 and Y is the intersection of X with r hyperplanes of P^n, with r \le d-1. Then, every formal rational function on X along Y can be (uniquely) extended to a rational function on X. Due to its importance, the aim of this paper is to provide two elementary global geometric proofs of this theorem.
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Cite
@article{arxiv.0810.1688,
title = {On a theorem of Faltings on formal functions},
author = {Paola Bonacini and Alessio del Padrone and Michele Nesci},
journal= {arXiv preprint arXiv:0810.1688},
year = {2008}
}
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9 pages