2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131661In 1962-63, M. Nagata showed that an abstract variety could be embedded into a complete variety. Later, P. Deligne translated Nagata's proof into the language of schemes, but did not publish his notes. This paper, which is to appear as an appendix in a forthcoming book, gives an elaboration of Deligne's notes. It also contains some complementary results on extending divisors and vector sheaves to suitable completions.amstex, 19 pagesAlgebraic Geometry14A15 (Primary) 14E99, 14J60 (Secondary)text