Finite type refers to a property of a coherent sheaf that indicates it can be generated by a finite number of sections over any open set. This means that there exists a finite set of generators for the sheaf that can be used to describe all its sections, making it a useful concept in algebraic geometry and sheaf theory. Finite type relates closely to the notion of finitely generated modules, ensuring manageable and coherent behavior of the sheaf in terms of its structure and applications.
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