On a locally Noetherian scheme, a coherent sheaf is a quasi-coherent sheaf that is locally associated with a finitely generated module. Kernels, cokernels, and finite direct sums of coherent sheaves remain coherent.
In algebraic geometry and related fields, a **coherent sheaf** is a specific type of sheaf that combines the properties of sheaves with certain algebraic conditions that make them suitable for studying geometric objects.
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