Coherent sheaves and cohesive sheaves

2008/08/12 by László Lempert, Lempert, Laszlo
Mathematics · #13C #14F05 #32B05 #32C35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0808.1717

openalex publication_date 2008/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider coherent and cohesive sheaves of \cO--modules over open sets Ω⊂\bCⁿ. We prove that coherent sheaves, and certain other sheaves derived from them, are cohesive; and conversely, certain sheaves derived from cohesive sheaves are coherent. An important tool in all this, also proved here, is that the sheaf of Banach space valued holomorphic germs is flat.

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