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closed immersion of schemes

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Definition

A homomorphism f:XYf:X\to Y of schemes is a closed immersion if it is tracked by a homeomorphism of the underlying topological space XX onto a closed subspace of YY, and the comorphism f :𝒪 Yf *𝒪 Xf^\sharp:\mathcal{O}_Y\to f_*\mathcal{O}_X is an epimorphism of sheaves on YY.

More generally, let us consider some category of spaces, i.e. sheaves of sets on C=AffC = Aff equipped with a subcanonical Grothendieck topology. Then a morphism FGF\to G of spaces is said to be closed immersion if it is representable by a strict monomorphism.

References

Discussion in the context of higher geometry/higher algebra is in

Last revised on August 30, 2020 at 11:09:44. See the history of this page for a list of all contributions to it.