Coherent Analytic Sheaves (Die Grundlehren der Mathematischen Wissenschaften)
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...Je mehr ich tiber die Principien der Functionentheorie nachdenke - und ich thue dies unablassig -, urn so fester wird meine Uberzeugung, dass diese auf dem Fundamente algebraischer Wahrheiten aufgebaut werden muss (WEIERSTRASS, Glaubensbekenntnis 1875, Math. Werke II, p. 235). 1. Sheaf Theory is a general tool for handling questions which involve local solutions and global patching. "La notion de faisceau s'introduit parce qu'il s'agit de passer de donnees 'locales' a l'etude de proprietes 'globales'" [CAR], p. 622. The methods of sheaf theory are algebraic. The notion of a sheaf was first introduced in 1946 by J. LERAY in a short note Eanneau d'homologie d'une representation, C. R. Acad. Sci. 222, 1366-68. Of course sheaves had occurred implicitly much earlier in mathematics. The "Monogene analytische Functionen", which K. WEIERSTRASS glued together from "Func- tionselemente durch analytische Fortsetzung", are simply the connected components of the sheaf of germs of holomorphic functions on a RIEMANN surface*'; and the "ideaux de domaines indetermines", basic in the work of K. OKA since 1948 (cf. [OKA], p. 84, 107), are just sheaves of ideals of germs of holomorphic functions. Highly original contributions to mathematics are usually not appreciated at first. Fortunately H. CARTAN immediately realized the great importance of LERAY'S new abstract concept of a sheaf. In the polycopied notes of his Semina ire at the E. N. S. Hardcover, Label: Springer-Verlag, Springer-Verlag, Produktgruppe: Book, Publiziert: 1984-10, Studio: Springer-Verlag, Verkaufsrang: 3936066.

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buecher.de GmbH & Co. KG, [1].
. . . Je mehr ich tiber die Principien der Functionentheorie nachdenke - und ich thue dies unablassig -, urn so fester wird meine Uberzeugung, dass diese auf dem Fundamente algebraischer Wahrheiten aufgebaut werden muss (WEIERSTRASS, Glaubensbekenntnis 1875, Math. Werke II, p. 235). 1. Sheaf Theory is a general tool for handling questions which involve local solutions and global patching. "La notion de faisceau s'introduit parce qu'il s'agit de passer de donnees 'locales' a l'etude de proprietes 'globales'" [CAR], p. 622. The methods of sheaf theory are algebraic. The notion of a sheaf was first introduced in 1946 by J. LERAY in a short note Eanneau d'homologie d'une representation, C. R. Acad. Sci. 222, 1366-68. Of course sheaves had occurred implicitly much earlier in mathematics. The "Monogene analytische Functionen", which K. WEIERSTRASS glued together from "Func tionselemente durch analytische Fortsetzung", are simply the connected components of the sheaf of germs of holomorphic functions on a RIEMANN surface*' and the "ideaux de domaines indetermines", basic in the work of K. OKA since 1948 (cf. [OKA], p. 84, 107), are just sheaves of ideals of germs of holomorphic functions. Highly original contributions to mathematics are usually not appreciated at first. Fortunately H. CARTAN immediately realized the great importance of LERAY'S new abstract concept of a sheaf. In the polycopied notes of his Semina ire at the E. N. S.Softcover reprint of the original 1st ed. 1984. 2011. XVIII, 249 pp. 235 mmVersandfertig in 3-5 Tagen, Softcover.

Von Händler/Antiquariat, Black Oak Books Holdings Corp. [53531808], El Cerrito, CA, U.S.A.
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Von Händler/Antiquariat, AHA-BUCH GmbH [51283250], Einbeck, NDS, Germany.
This item is printed on demand - Print on Demand Titel. Neuware - 1. Complex Spaces.- 1. The Notion of a Complex Space.- 0. Ringed Spaces 1. The Space ( n, (O) 2. Zero Sets and Complex Model Spaces 3. Sheaves of Local -Algebras. -ringed Spaces 4. Morphisms of -ringed Spaces 5. Complex Spaces 6. Sections and Functions 7. Construction of Complex Spaces by Gluing 8. The Complex Projective Space n 9. Historical Notes.- 2. General Properties of Complex Spaces.- 1. Zero Sets of Ideal Sheaves 2. Closed Complex Subspaces 3. Factorization of Holomorphic Maps 4. Complex Spaces and Coherent Analytic Sheaves. Extension Principle 5. Analytic Image Sheaves 6. Analytic Inverse Image Sheaves 7. Holomorphic Embeddings.- 3. Direct Products and Graphs.- 1. The Bijection ol(X, n) O(X)n. Extension of Holomorphic Maps 2. Complex Direct Products 3. Existence of Canonical Products. Local Case 4. Existence of Canonical Products. Global Case 5. Graph Space of a Holomorphic Map.- 4. Complex Spaces and Cohomology.- 1. Divisors 2. Holomorphic Vector Bundles 3. Line Bundles and Divisors 4. Holomorphically Convex Spaces and Stein Spaces 5. ech Cohomology of Analytic Sheaves 6. Cohomology of Coherent Sheaves with Respect to Stein Coverings 7. Higher Dimensional Direct Images.- 2. Local Weierstrass Theory.- 1. The Weierstrass Theorems.- 0. Generalities 1. The WeierstraB Division Theorem 2. The Weierstraß Preparation Theorem 3. A Simple Observation.- 2. Algebraic Structure of $${O_{{C^n},0}}$$.- 1. Noether Property and Factoriality 2. Hensel s Lemma 3. Closedness of Sub-modules.- 3. Finite Maps.- 1. Closed Maps 2. Finite Maps. Local Description 3. Local Representation of Image Sheaves 4. Exactness of the Functor f for Finite Maps 5. Weierstraß Maps.- 4. The Weierstrass Isomorphism.- 1. The Generalized Weierstraß Division Theorem 2. The Weierstraß Isomorphism 3. A Coherence Lemma 4. A Further Generalization of the Generalized Weierstraß Division Theorem.- 5. Coherence of Structure Sheaves.- 1. Formal Coherence Criterion 2. The Coherence of $${O_{{C^n}}}$$ 3. Coherence of all Structure Sheaves OX.- 3. Finite Holomorphic Maps.- 1. Finite Mapping Theorem.- 1. Projection Lemma 2. Finite Holomorphic Maps and Isolated Points 3. Finite Mapping Theorem.- 2. Rückert Nullstellensatz for Coherent Sheaves.- 1. Preliminary Version 2. Rückert Nullstellensatz.- 3. Finite Open Holomorphic Maps.- 1. A Necessary Condition for Openness 2. Torsion Sheaves and Criterion of Openness 3. Coherence of Torsion Sheaves and Open Mapping Lemma 4. Existence of Finite Open Projections.- 4. Local Description of Complex Subspaces in n.- 1. The Local Description Lemma 2. Proof of the Local Description Lemma.- 4. Analytic Sets. Coherence of Ideal Sheaves.- 1. Analytic Sets and their Ideal Sheaves.- 1. Analytic Sets 2. Ideal Sheaf of an Analytic Set 3. Local Decomposition Lemma 4. Prime Components. Criterion of Reducibility 5. Rückert Nullstellensatz for Ideal Sheaves 6. Analytic Sets and Finite Holomorphic Maps.- 2. Coherence of the Sheaves i (A).- 1. Proof of Coherence in a Special Case 2. Reduction to Analytic Sets in Domains of n 3. Further Reduction to a Lemma 4. Verification of the Assumptions of Lemma 3 5. Coherence of Radical Sheaves.- 3. Applications of the Fundamental Theorem and of the Nullstellensatz.- 1. Analytic Sets and Reduced Closed Complex Subspaces 2. Reduction of Complex Spaces 3. Reduced Complex Spaces.- 4. Coherent and Locally Free Sheaves.- 1. Corank of a Coherent Sheaf 2. Characterization of Locally Free Sheaves.- 5. Dimension Theory.- 1. Analytic and Algebraic Dimension.- 1. Analytic Dimension of Complex Spaces. Upper Semi-Continuity 2. Analytic and Algebraic Dimension 3. Dimension of the Reduction and of Analytic Sets.- 2. Active Germs and the Active Lemma.- 1. The Sheaf of Active Germs 2. Criterion of Activity 3. Existence of Active Functions. Lifting Lemma 4. Active Lemma.- 3. Applications of the Active Lemma.- 1. Basic Properties of Dimension. Ritt s Lemma 2. Analytic.

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