Local Fields
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Local Fields
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Author : Jean-Pierre Serre
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Local Fields written by Jean-Pierre Serre 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.
The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray.
Local Fields
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Author : John William Scott Cassels
language : en
Publisher: Cambridge University Press
Release Date : 1986-08-21
Local Fields written by John William Scott Cassels and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-08-21 with Mathematics categories.
This book provides a fairly elementary and self-contained introduction to local fields.
Local Fields And Their Extensions Second Edition
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Author : Ivan B. Fesenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-07-17
Local Fields And Their Extensions Second Edition written by Ivan B. Fesenko 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 2002-07-17 with Mathematics categories.
This book offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods. It has been ten years since the publication of the first edition, and, according to Mathematical Reviews, 1,000 papers on local fields have been published during that period. This edition incorporates improvements to the first edition, with 60 additional pages reflecting several aspects of the developments in local number theory. The volume consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor -groups of fields and of local fields. The first three parts essentially simplify, revise, and update the first edition. The book includes the following recent topics: Fontaine-Wintenberger theory of arithmetically profinite extensions and fields of norms, explicit noncohomological approach to the reciprocity map with a review of all other approaches to local class field theory, Fesenko's -class field theory for local fields with perfect residue field, simplified updated presentation of Vostokov's explicit formulas for the Hilbert norm residue symbol, and Milnor -groups of local fields. Numerous exercises introduce the reader to other important recent results in local number theory, and an extensive bibliography provides a guide to related areas.
Local Class Field Theory
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Author : Kenkichi Iwasawa
language : en
Publisher: Oxford University Press, USA
Release Date : 1986
Local Class Field Theory written by Kenkichi Iwasawa and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with History categories.
This readable introduction to local class field theory, a theory of algebraic extensions, covers such topics as abelian extensions. Almost self-contained, the book is accessible to any reader with a basic background in algebra and topological groups.
Fourier Analysis On Local Fields Mn 15
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Author : M. H. Taibleson
language : en
Publisher: Princeton University Press
Release Date : 2015-03-08
Fourier Analysis On Local Fields Mn 15 written by M. H. Taibleson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-08 with Mathematics categories.
This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (real and complex numbers); the rest are local fields (p-adic numbers, p-series fields, and their algebraic extensions). The local fields are studied in an effort to extend knowledge of the reals and complexes as locally compact fields. The author's central aim has been to present the basic facts of Fourier analysis on local fields in an accessible form and in the same spirit as in Zygmund's Trigonometric Series (Cambridge, 1968) and in Introduction to Fourier Analysis on Euclidean Spaces by Stein and Weiss (1971). Originally published in 1975. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Arithmetic And Geometry Over Local Fields
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Author : Bruno Anglès
language : en
Publisher: Springer Nature
Release Date : 2021-03-03
Arithmetic And Geometry Over Local Fields written by Bruno Anglès and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-03 with Mathematics categories.
This volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics.
A Gentle Course In Local Class Field Theory
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Author : Pierre Guillot
language : en
Publisher: Cambridge University Press
Release Date : 2018-11
A Gentle Course In Local Class Field Theory written by Pierre Guillot and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11 with Mathematics categories.
A self-contained exposition of local class field theory for students in advanced algebra.
Local Fields And Their Extensions
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Author : Ivan B. Fesenko
language : en
Publisher:
Release Date : 1993
Local Fields And Their Extensions written by Ivan B. Fesenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Algebraic fields categories.
This book offers a modern presentation of local fields whose spectacular development was initiated almost one hundred years ago by K. Hensel. The volume consists of nine chapters divided into four parts: arithmetic properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor K-groups of fields and of local fields. The first three parts essentially simplify, revise, and update the first edition. This second edition contains about sixty additional pages reflecting several aspects of the developments in.
Proceedings Of A Conference On Local Fields
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Author : T. A. Springer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Proceedings Of A Conference On Local Fields written by T. A. Springer 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.
From July 25-August 6, 1966 a Summer School on Local Fields was held in Driebergen (the Netherlands), organized by the Netherlands Universities Foundation for International Cooperation (NUFFIC) with financial support from NATO. The scientific organizing Committl!e consisted ofF. VANDER BLIJ, A.H.M. LEVELT, A.F. MaNNA, J.P. MuRRE and T.A. SPRINGER. The Summer School was attended by approximately 80 mathematicians from various countries. The contributions collected in the present book are all based on the talks given at the Summer School. It is hoped that the book will serve the same purpose as the Summer School: to provide an introduction to current research in Local Fields and related topics. July 1967 T.A. SPRINGER Contents ARnN, M. and B. MAZUR: Homotopy of Varieties in the Etale Topology 1 BAss, H: The Congruence Subgroup Problem 16 BRUHAT, F. et J. TITs: Groupes algebriques simples sur un corps local . 23 CASSELS, J.W.S. : Elliptic Curves over Local Fields 37 DwoRK, B. : On the Rationality of Zeta Functions and L-Series 40 MaNNA, A.F. : Linear Topological Spaces over Non-Archimedean Valued Fields . 56 NERON, A. : Modeles minimaux des espaces principaux homo genes sur les courbes elliptiques 66 RAYNAUD, M. : Passage au quotient par une relation d'equivalence plate . 78 REMMERT, R. : Algebraische Aspekte in der nichtarchimedischen Analysis . 86 SERRE, J.-P. : Sur les groupes de Galois attaches aux groupes p-divisibles . 118 SWINNERTON-DYER, P. : The Conjectures of Birch and Swinnerton- Dyer, and of Tate . 132 TATE, J.T.
Harmonic Analysis And Fractal Analysis Over Local Fields And Applications
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Author : Su Weiyi
language : en
Publisher: World Scientific
Release Date : 2017-08-17
Harmonic Analysis And Fractal Analysis Over Local Fields And Applications written by Su Weiyi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-17 with Mathematics categories.
This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.