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

中文翻译：

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相干滑轮的分裂引理

所提出的分裂引理扩展了 Gromov 和 Forstnerič 的技术，以粘合给定分析层的局部部分，这是证明所有 Oka 原理的关键步骤。证明所依赖的新颖性是相干滑轮过渡图的提升引理，这将证明简化为 Forstnerič 的工作。作为应用，我们在 Forster 和 Ramspott 的可容许对的 Oka 原理和椭圆浸没部分的插值性质的证明中获得了捷径，这是由 Forstnerič 和 Prezelj 获得的 Gromov 结果的扩展。