Why has been introducted the term coherent in sheaf theory? What's its intuitive significance? In italian we translate it with the term "coerente", in the sense of compactness.
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I don't know Italian or French, but if coherente is also cognate to the French for compact, then this could correspond to the sense of compact as "topologically finite." – Kevin Carlson Jan 27 '15 at 07:31
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So, the fact that a coherent sheaf is a sheaf of $\mathfrak{O}-$modules of finite type implies, intuitively, the topologically finiteness? – TheWanderer Jan 27 '15 at 07:34
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3See http://mathoverflow.net/questions/44042/whats-coherent-about-coherent-sheaves – Mariano Suárez-Álvarez Jan 27 '15 at 07:36