Local Analytic Geometry
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Local Analytic Geometry
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Author :
language : en
Publisher:
Release Date : 1964
Local Analytic Geometry written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Geometry, Analytic categories.
Local Analytic Geometry
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Author : Theo de Jong
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Local Analytic Geometry written by Theo de Jong and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
Algebraic geometry is, loosely speaking, concerned with the study of zero sets of polynomials (over an algebraically closed field). As one often reads in prefaces of int- ductory books on algebraic geometry, it is not so easy to develop the basics of algebraic geometry without a proper knowledge of commutative algebra. On the other hand, the commutative algebra one needs is quite difficult to understand without the geometric motivation from which it has often developed. Local analytic geometry is concerned with germs of zero sets of analytic functions, that is, the study of such sets in the neighborhood of a point. It is not too big a surprise that the basic theory of local analytic geometry is, in many respects, similar to the basic theory of algebraic geometry. It would, therefore, appear to be a sensible idea to develop the two theories simultaneously. This, in fact, is not what we will do in this book, as the "commutative algebra" one needs in local analytic geometry is somewhat more difficult: one has to cope with convergence questions. The most prominent and important example is the substitution of division with remainder. Its substitution in local analytic geometry is called the Weierstraft Division Theorem. The above remarks motivated us to organize the first four chapters of this book as follows. In Chapter 1 we discuss the algebra we need. Here, we assume the reader attended courses on linear algebra and abstract algebra, including some Galois theory.
Local Analytic Geometry
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Author : Shreeram Shankar Abhyankar
language : en
Publisher: World Scientific
Release Date : 2001
Local Analytic Geometry written by Shreeram Shankar Abhyankar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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.
Local Analytic Geometry
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Author : Theo de Jong
language : en
Publisher:
Release Date : 2000
Local Analytic Geometry written by Theo de Jong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Geometry, Analytic categories.
Local Analytic Geometry
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Author : Dimitris N. Chorafas
language : en
Publisher:
Release Date : 1964
Local Analytic Geometry written by Dimitris N. Chorafas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with categories.
Analysis Geometry Number Theory The Mathematics Of Leon Ehrenpreis
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Author : Eric Grinberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Analysis Geometry Number Theory The Mathematics Of Leon Ehrenpreis written by Eric Grinberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book presents the proceedings from the conference honoring the work of Leon Ehrenpreis. Professor Ehrenpreis worked in many different areas of mathematics and found connections among all of them. For example, one can find his analytic ideas in the context of number theory, geometric thinking within analysis, transcendental number theory applied to partial differential equations, and more. The conference brought together the communities of mathematicians working in the areas of interest to Professor Ehrenpreis and allowed them to share the research inspired by his work. The collection of articles here presents current research on PDEs, several complex variables, analytic number theory, integral geometry, and tomography. The work of Professor Ehrenpreis has contributed to basic definitions in these areas and has motivated a wealth of research results. This volume offers a survey of the fundamental principles that unified the conference and influenced the mathematics of Leon Ehrenpreis.
Handbook Of Geometry And Topology Of Singularities Iv
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Author : José Luis Cisneros-Molina
language : en
Publisher: Springer Nature
Release Date : 2023-10-07
Handbook Of Geometry And Topology Of Singularities Iv written by José Luis Cisneros-Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-07 with Mathematics categories.
This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Local Analytic Geometry
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Author : Theo De Jong
language : en
Publisher:
Release Date : 2014-01-15
Local Analytic Geometry written by Theo De Jong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Linear Inequalities In Local Analytic Geometry
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Author : Ti Wang
language : en
Publisher:
Release Date : 1992
Linear Inequalities In Local Analytic Geometry written by Ti Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Representations Of Algebras Locally Compact Groups And Banach Algebraic Bundles
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Author : J. M.G. Fell
language : en
Publisher: Academic Press
Release Date : 1988-04-15
Representations Of Algebras Locally Compact Groups And Banach Algebraic Bundles written by J. M.G. Fell and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-04-15 with Mathematics categories.
This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.