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Differential Calculus on Analytic Spaces
The Finiteness Theorem
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4-module algebraic analytic ring analytic set analytic space Banach space Banach vector bundles bundle morphism closed analytic subspace coherent analytic sheaf coherent sheaf cohomology commutative compact complex manifold complex space consider continuous Corollary defined Definition denote differential operator elements exact sequence Example exists fiber finite morphism flat Frechet space free resolution germs of analytic germs of holomorphic given Grauert hence holomorphic functions holomorphic map hyperplane section induced inductive limit injective Krull topology Lemma Let F line bundle linear Math maximal ideal meromorphic function meromorphic mapping module morphic morphism of analytic neighbourhood noetherian open neighborhood open set open subset polycylinder proof of Theorem proper Proposition prove reduced analytic space resp restriction ringed space sheaf of germs sheaf of ideals sheaves Stein covering Stein manifold Suppose surjective Tort vector bundle morphism weakly holomorphic zero