Gluing Schemes and a Scheme Without Closed Points

  title={Gluing Schemes and a Scheme Without Closed Points},
  author={Karl Schwede},
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 fibered 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. 

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