UID:
almahu_9947366701502882
Format:
1 online resource (503 p.)
ISBN:
1-281-76632-1
,
9786611766320
,
0-08-087326-X
Series Statement:
Pure and applied mathematics; a series of monographs and textbooks ; 14
Note:
Originally published: New York : Academic Press, c1964, in series Pure and applied mathematics (Academic Press) ; 14.
,
Front Cover; Local Analytic Geometry; Copyright Page; Contents; Preface; Instructions to the Reader; Chapter I. Elementary Theory in Cn; 1. Notation and Terminology; 2. Convergent Power Series; 3. Laurent Series; 4. Cauchy Theory; 5. Convexity in Rn; 6. Laurent Expansion in Cn; 7. Domains of Holomorphy; 8. A Theorem of Rad?; 9. Comments on Totally Disconnected Fields; Chapter II. Weierstrass Preparation Theorem; 10. Weierstrass Preparation Theorem. Identity Theorem. Finite Ideal Bases and Unique Factorization in Power Series Rings. Implicit Function Theorem
,
11. Continuity of Roots and Open Map Theorem; 12. Hensel's Lemma. Continuity of Algebroid Functions; 13. Complex Weierstrass Preparation Theorem; 14. Riemann Extension Theorem and Connectivity of Algebroid Hypersurfaces; 15. Oka Coherence; 16. Cartan Module Bases; Chapter III. Review from Local Algebra; 17. Depth, Height, and Dimension. Completions. Direct Sums. Resultants and Discriminants; 18. Quotient Rings; 19. Integral Dependence and Finite Generation; 20. Henselian Rings; 21. Order and Rank in Local Rings. Regular Local Rings
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22. Another Proof that a Formal Power Series Rings is Noetherian; Chapter IV. Parameters in Power Series Rings; 23. Parameters for Ideals; 24. Perfect Fields; 25. Regularity of Quotient Rings; 26. Translates of Ideals; 27. Dimension of an Intersection; 28. Algebraic Lemmas on Algebroid Functions; Chapter V. Analytic Sets; 29. The Language of Germs; 30. Decomposition of an Analytic Set Germ; 31. Rückert-Weierstrass Parametrization of an Irreducible Analytic Set Germ; 32. Rückert-Weierstrass Parametrization of an Irreducible Analytic Set Germ (Summary); 33. Local Properties of Analytic Sets
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34. Connectivity Properties of Complex Analytic Sets; 35. Parametrization of a Pure Dimensional Analytic Set; 36. Normal Points of Complex Analytic Sets. Remarks on Algebraic Varieties; 37. Remmert-Stein-Thullen Theorem on Essential Singularities of Complex Analytic Sets. Theorem of Chow; 38. Topological Dimension; 39. Remarks on the Fundamental Group; Chapter VI. Language of Sheaves; 40. Inductive Systems and Presheaves; 41. Sheaves; 42. Coherent Sheaves; Chapter VII. Analytic Spaces; 43. Definitions; 44. Recapitulation of Properties of Analytic Spaces; 45. Invariance of Order and Rank; 46. Bimeromorphic Maps and Normalizations; Bibliography; Index of Notation; Subject Index
Additional Edition:
ISBN 0-12-374564-0
Language:
English
