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Local Fields (Graduate Texts in Mathematics) - Jean-Pierre Serre, Marvin J. Greenberg
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[SR: 1233299], Hardcover, [EAN: 9780387904245], Springer, Springer, Book, [PU: Springer], Springer, 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., 13887, Algebra, 13889, Abstract, 13893, Elementary, 13897, Intermediate, 13899, Linear, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 13963, Number Theory, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 491542, Algebra & Trigonometry, 468218, Mathematics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books

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Local Fields - Jean-Pierre Serre
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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 Buch (fremdspr.) Bücher>Fremdsprachige Bücher>Englische Bücher, Springer

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Local fields serie graduate texts in mathematics volume 67 - Serre, j.p.
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Local fields serie graduate texts in mathematics volume 67 - neues Buch

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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 i, [PU: Springer]

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Local Fields: 67 (Graduate Texts in Mathematics) - Jean-Pierre Serre, Marvin J. Greenberg
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[SR: 868693], Hardcover, [EAN: 9780387904245], Springer, Springer, Book, [PU: Springer], 1980-01-19, Springer, 278321, Algebra, 278320, Mathematics, 57, Science & Nature, 1025612, Subjects, 266239, Books, 922522, Mathematical Theory, 922518, Chaos, 278381, Game Theory, 278320, Mathematics, 57, Science & Nature, 1025612, Subjects, 266239, Books, 922942, Maths, 922868, Popular Science, 57, Science & Nature, 1025612, Subjects, 266239, Books, 564352, Mathematics, 570902, Algebra, 570874, Applied Mathematics, 570912, Calculus & Mathematical Analysis, 570934, Combinatorics & Graph Theory, 570936, Geometry, 570964, Mathematical Theory, 564334, Scientific, Technical & Medical, 1025612, Subjects, 266239, Books

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Local Fields Local-Fields~~Marvin-J-Greenberg Science>Mathematics>Mathematics Hardcover, Springer New York

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Local Fields
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BContents:/B Basic results on discrete valuation rings, Dedekind domains, and completions.-BRRamification theory: discriminant, different, ramification subgroups, Hasse-Arf theorem, Artin representations.-BRGroup cohomology, with emphasis on arithmetical applications: theorems of Tate and Nakayama, Galois cohomology, class formations.-BRLocal class field theory, presented from the cohomological point of view. The main result is the determination of the topological Galois group of the maximal abelian extension.

Detailangaben zum Buch - Local Fields


EAN (ISBN-13): 9780387904245
ISBN (ISBN-10): 0387904247
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2007
Herausgeber: Springer-Verlag GmbH
260 Seiten
Gewicht: 0,567 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 06.06.2007 20:49:43
Buch zuletzt gefunden am 02.09.2017 23:18:35
ISBN/EAN: 9780387904245

ISBN - alternative Schreibweisen:
0-387-90424-7, 978-0-387-90424-5


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