Local Analytic Geometry PDF
By:Shreeram Shankar Abhyankar
Published on 2001 by World Scientific
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from number theory. When it is specialized to the complex case, connectivity and other topological properties come to the fore. In particular, via singularities of analytic sets, topological fundamental groups can be studied. In the transition from punctual to local, i.e. from properties at a point to properties near a point, the classical work of Osgood plays an important role. This gives rise to normic forms and the concept of the Osgoodian. Following Serre, the passage from local to global properties of analytic spaces is facilitated by introducing sheaf theory. Here the fundamental results are the coherence theorems of Oka and Cartan. They are followed by theory normalization due to Oka and Zariski in the analytic and algebraic cases, respectively. Contents: Elementary Theory in Cn; Weierstrass Preparation Theorem; Review from Local Algebra; Parameters in Power Series Rings; Analytic Sets; Language of Sheaves; Analytic Spaces. Readership: Graduate students and researchers in pure mathematics.
This Book was ranked at 28 by Google Books for keyword Analytic.
Book ID of Local Analytic Geometry's Books is 7apjpUgZqJUC, Book which was written byShreeram Shankar Abhyankarhave ETAG "ReuWoSvdWR0"
Book which was published by World Scientific since 2001 have ISBNs, ISBN 13 Code is 9789812810342 and ISBN 10 Code is 981281034X
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Book which have "504 Pages" is Printed at BOOK under CategoryMathematics
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