A-coherent sheaves on a ringed space correspond to finitely presented modules over the global sections ring under flatness and exactness of global sections, enabling a proof of faithful flatness from Nash to analytic function rings via Cartan's Theorem B.
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Algebraic Geometry over Non-Algebraically Closed Fields -- A-Coherent Sheaves over a Ringed Space
A-coherent sheaves on a ringed space correspond to finitely presented modules over the global sections ring under flatness and exactness of global sections, enabling a proof of faithful flatness from Nash to analytic function rings via Cartan's Theorem B.