Abstract
We begin with a digression on some general facts about sheaves. Let F,G be sheaves of abelian groups on the topological space X, φ: F → G a morphism. For U open, we let K(U) = Ker(F(U) → G(U)); it is easy to check that K is a sheaf, which we call the kernel of φ. We say φ is injective if K = O, i.e., if F(U) → G(U) is injective for all U. It is easily seen that this holds if and only if all the maps φX:F X → G X on stalks are injective.
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© 1988 Springer-Verlag Berlin Heidelberg
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Mumford, D. (1988). Closed subpreschemes. In: The Red Book of Varieties and Schemes. Lecture Notes in Mathematics, vol 1358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21581-4_15
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DOI: https://doi.org/10.1007/978-3-662-21581-4_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50497-9
Online ISBN: 978-3-662-21581-4
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