Local analytic geometry /

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Bibliographic Details
Author / Creator:Abhyankar, Shreeram Shankar.
Imprint:Singapore ; River Edge, NJ : World Scientific, ©2001.
Description:1 online resource (xv, 488 pages) : illustrations
Series:Pure and applied mathematics; a series of monographs and textbooks ; 14
Pure and applied mathematics (Academic Press) ; 14.
Subject:Geometry, Analytic.
Functional analysis.
MATHEMATICS -- Geometry -- Analytic.
Functional analysis.
Geometry, Analytic.
Electronic book.
Electronic books.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11217937
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Notes:Includes bibliographical references (pages 471-474) and indexes.
Print version record.
Summary: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.
Other form:Print version: Abhyankar, Shreeram Shankar. Local analytic geometry. Singapore ; River Edge, NJ : World Scientific, ©2001