# Ag.algebraische Geometrie – A naive question about Serres GAGA

To let $$X, Y$$ to be a complex, affine strain and $$X ^ h, Y ^ h$$ the analysis schemes assigned to them. To let $$f: X ^ h to Y ^ h$$ Be a biholomorphic analytical map of analytic schemes. Is it true then (via Serre's GAGA) that there is a 1-1 match between the connected sheaves $$X$$ and that on $$Y$$? In other words, the withdrawal of a coherent sheaf is on $$Y ^ h$$, again a coherent sheaf over $$X ^ h$$? Every note is welcome.