Homomorphisms of infinitely generated analytic sheaves

Vakhid Masagutov Department of Mathematics, Purdue University

K-Theory and Homology mathscidoc:1701.20004

Arkiv for Matematik, 49, (1), 129-148, 2009.4
We prove that every homomorphism $\mathcal{O}^{E}_{\zeta}\rightarrow\mathcal{O}^{F}_{\zeta}$ , with$E$and$F$Banach spaces and ζ∈ℂ^{$m$}, is induced by a $\mathop{\mathrm{Hom}}(E,F)$ -valued holomorphic germ, provided that 1≤$m$<∞. A similar structure theorem is obtained for the homomorphisms of type $\mathcal{O}^{E}_{\zeta}\rightarrow\mathcal{S}_{\zeta}$ , where $\mathcal{S}_{\zeta}$ is a stalk of a coherent sheaf of positive depth. We later extend these results to sheaf homomorphisms, obtaining a condition on coherent sheaves which guarantees the sheaf to be equipped with a unique analytic structure in the sense of Lempert–Patyi.
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  title={Homomorphisms of infinitely generated analytic sheaves},
  author={Vakhid Masagutov},
  booktitle={Arkiv for Matematik},
Vakhid Masagutov. Homomorphisms of infinitely generated analytic sheaves. 2009. Vol. 49. In Arkiv for Matematik. pp.129-148. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203629718825997.
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