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Gluing schemes and a scheme without closed points. (English) Zbl 1216.14003

Kachi, Yasuyuki (ed.) et al., Recent progress in arithmetic and algebraic geometry. Proceedings of the 31st annual Barrett lecture series conference, Knoxville, TN, USA, April 25–27, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3401-0/pbk). Contemporary Mathematics 386, 157-172 (2005).
Summary: We first construct and give basic properties of a fibered coproduct in the category of ringed spaces (which is just a particular type of colimit). We then look at some special cases where this actually gives a fibred coproduct in the category of schemes. Intuitively this is gluing a collection of schemes along some collection of other schemes (possibly subschemes). We then use this to construct a scheme without closed points.
For the entire collection see [Zbl 1078.14002].

MSC:

14A15 Schemes and morphisms
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