The Journal of Geometric Analysis

, Volume 29, Issue 1, pp 577–615 | Cite as

Cartan Theorems for Stein Manifolds Over a Discrete Valuation Base

  • Jari TaskinenEmail author
  • Kari Vilonen


Let X be a complex manifold, let A be a topological discrete valuation ring, and write Open image in new window for the sheaf of functions on X with values in A. We prove Cartan theorems A and B for coherent Open image in new window -modules, when X is a Stein manifold and A satisfies some requirements like being a nuclear direct limit of Banach algebras. The result is motivated by questions in the work of the second author with Kashiwara in the proof of the codimension-three conjecture for holonomic microdifferential systems.


Cartan theorem A and B Stein manifold Coherent module Codimension-three conjecture Discrete valuation ring Banach algebra Inductive limit 

Mathematics Subject Classification

Primary 32C35 Secondary 32W05 46A13 46H99 


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© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  2. 2.School of Mathematics and StatisticsUniversity of MelbourneMelbourneAustralia

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