Descent of dg cohesive modules for open covers on complex manifolds

2018/04/01 by Zhaoting Wei, Wei, Zhaoting · 1 citation
Mathematics · #18D20 #18G55 #46L87 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1804.00993

openalex publication_date 2018/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the descent problem of cohesive modules on complex manifolds. For a complex manifold X we could consider the Dolbeault dg-algebra A(X) on it and Block in 2006 introduced a dg-category P_A(X), called cohesive modules, associated with A(X). The same construction works for any open subset U⊂ X and we obtain a dg-presheaf on X given by U↦ P_A(U). In this paper we prove that this dg-presheaf satisfies the descent property for any locally finite open cover of a complex manifold X. This generalizes part of the results of Ben-Bassat and Block in 2012, which studied the case that X is covered by two open subsets.

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