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Finitude cohomologique des morphismes propres en géométrie algébrique : une preuve transcendante sans techniques projectives

Antoine Ducros
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Abstract

We propose here a transcendantal proof of the coherence of the higher direct images of a coherent sheaf by a proper morphism of algebraic varieties, which does not use Chow's lemma nor any projective method. The main tool here are comparison with coherent cohomology of a (Berkovich) analytic space over a trivially valued field, and Kiehls' theorem about the proper morphisms between rigid-analytic spaces.

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Antoine Ducros. 2006-12-18. Finitude cohomologique des morphismes propres en géométrie algébrique : une preuve transcendante sans techniques projectives. https://arxiv.org/abs/math/0612521

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