Coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. Basic constructions of... · Local behavior of coherent...

27 июл. 2023 г. · A coherent sheaf of modules is a geometric globalization of the notion of coherent module. 2. Definition Over a ringed topos

If M is finitely generated, then ˜M is coherent. It is convenient to define a sheaf of form ˜M, where M is not necessarily finitely generated to be ...

For a sheaf of A -modules, being coherent is equivalent to being locally isomorphic to the cokernel of a homomorphism φ : A q → A p. The necessity part is ...

Although it is possible to consider coherent sheaves on non-Noetherian schemes we will always assume the base scheme is locally Noetherian when we consider ...

6 янв. 2022 г. · A structure sheaf O is called a coherent sheaf of rings if O is coherent as a sheaf of modules over itself, which reduces to condition 2).

In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions with ...

The category of coherent sheaves on a ringed space X is a more reasonable object than the category of quasi-coherent sheaves.

27 дек. 2020 г. · First of all, if O is coherent over itself, then a sheaf of O-modules is coherent if and only if it is locally finitely presented.

22 мар. 2013 г. · If M M is a finitely generated module, then ~M M ~ is called coherent. A sheaf on an arbitrary scheme X X is called (quasi ...