semicoherence
Semicoherence is a finiteness condition for sheaves of modules on a ringed space, used mainly in complex analytic geometry and algebraic geometry. It serves as a relaxation of coherence, allowing certain infinite-type sheaves to retain enough finiteness control for practical work.
One standard way to formulate semicoherence is this: a sheaf F of OX-modules is semi-coherent if, for
Relations to other notions are straightforward. Every coherent sheaf is semi-coherent, since coherence is a stronger
Examples and behavior: the structure sheaf OX is semi-coherent, and, in many settings, coherent sheaves are semi-coherent
See also: coherent sheaf, quasi-coherent sheaf, coherence theorems in analytic and algebraic geometry.