A splitting lemma for coherent sheaves

The presented splitting lemma extends the techniques of Gromov and Forstneri\v{c} to glue local sections a given analytic sheaf, key step in proof all Oka principles. novelty on which depends is lifting for transition maps coherent sheaves, yields reduction work Forstneri\v{c}. As applications we get shortcuts proofs Forster Ramspott's principle admissible pairs interpolation property elliptic submersions, an extension Gromov's results obtained by Prezelj.