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Local Analytic Geometry by Shreeram Shankar Abhyankar (Purdue Univ, Usa) at Abbey's Bookshop,
Local Analytic Geometry
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Shreeram Shankar Abhyankar (Purdue Univ, Usa)

Local Analytic Geometry

Shreeram Shankar Abhyankar (Purdue Univ, Usa)

$325.99

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English
World Scientific Publishing Co Pte Ltd
16 January 2001
Analytic geometry
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: algebraic treatment of several complex variables; geometric approach to algebraic geometry via analytic sets; survey of local algebra; and 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, ie. 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.
By:  
Imprint:   World Scientific Publishing Co Pte Ltd
Country of Publication:   Singapore
Edition:   New edition
Dimensions:   Height: 230mm,  Width: 163mm,  Spine: 32mm
Weight:   789g
ISBN:   9789810245054
ISBN 10:   981024505X
Pages:   504
Publication Date:  
Audience:   College/higher education ,  Professional and scholarly ,  Further / Higher Education ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Elementary Theory in Cn; Weierstrass Preparation Theorem; Review from Local Algebra; Parameters in Power Series Rings; Analytic Sets; Language of Sheaves; Analytic Spaces.

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