Sheaf Extension - Definition

Definition

Let X be a scheme, and let F, H be sheaves (of modules) on X. An extension of H by F is a short exact sequence of sheaves

Note that an extension is not determined by the sheaf G alone: The morphisms are also important.

A simple example of an extension of H by F is the sequence

where the second arrow is the inclusion and the fourth arrow is the projection onto the second summand. This extension is sometimes called trivial.

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