On a theorem of Faltings on formal functions

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dc.creatorBonacini, Paola
dc.creatordel Padrone, Alessio
dc.creatorNesci, Michele
dc.date2008-10-09
dc.date.accessioned2026-07-07T10:08:47Z
dc.date.available2026-07-07T10:08:47Z
dc.descriptionIn 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.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/0810.1688
dc.identifierhttp://arxiv.org/abs/0810.1688
dc.identifierLe Matematiche (Catania) Vol. LXII (2007) - Fasc. I, pp. 95-104
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171116
dc.subjectAlgebraic Geometry
dc.subject14B20; 14N05
dc.titleOn a theorem of Faltings on formal functions
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