Last edited by Nikolrajas

Tuesday, May 12, 2020 | History

3 edition of **Cohomology of number fields** found in the catalog.

Cohomology of number fields

JГјrgen Neukirch

- 67 Want to read
- 14 Currently reading

Published
**2008**
by Springer in Berlin
.

Written in English

- Algebraic fields,
- Galois theory,
- Homology theory

**Edition Notes**

Includes bibliographical references (p. [805]-819) and index.

Statement | Jürgen Neukirch, Alexander Schmidt, Kay Wingberg. |

Series | Grundlehren der mathematischen Wissenschaften -- 323 |

Contributions | Schmidt, Alexander, 1965-, Wingberg, Kay. |

Classifications | |
---|---|

LC Classifications | QA247 .N523 2008 |

The Physical Object | |

Pagination | xv, 825 p. : |

Number of Pages | 825 |

ID Numbers | |

Open Library | OL18817946M |

ISBN 10 | 9783540378884 |

LC Control Number | 2008921043 |

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Question about Neukirch's book Cohomology of Number Fields. Ask Question Asked 9 months ago. Active 9 months ago. Vol Number 2, April–June , Pages – COHOMOLOGY OF NUMBER FIELDS AND ANALYTIC PRO-p-GROUPS CHRISTIAN MAIRE Abstract. In this work, we are interested in the tame version of the Fontaine–Mazur conjecture. By viewing the pro-p-proup GS as a quo-tient of a Galois extension ramiﬁed at p and S, we obtain a connection.

We now begin the development of cohomology in number theory. As a ground field we take a nonarchimedean local field k, i.e. a field which is complete with respect to a discrete valuation and has a finite residue covers two cases, namely p-adic local fields, i.e. finite extensions of \(\mathbb{Q}_{p}\) for some prime number p, and fields of formal Laurent series \(\mathbb{F}((t Cited by: 1. ( views) Lectures On Galois Cohomology of Classical Groups by M. Kneser - Tata Institute of Fundamental Research, The main result is the Hasse principle for the one-dimensional Galois cohomology of simply connected classical groups over number fields. For most groups, this result is closely related to other types of Hasse principle.

In algebraic number theory and class field theory, you mainly need the cohomology of finite groups, which in fact is a very good place to start, so my advice would be to first study thoroughly the cohomology of finite groups, as for example, in Part 3 of Serre's book Local Fields (Corps Locaux). Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their -theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function properties, such as whether a ring admits.

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A wonderful monograph and reference in cohomology of number fields，authoritative and well written for any mathematician and graduate student working in number theory.

By the way，the printing quality of this second edition is also marvelous ，but the price is too by: Cohomology of Number Fields (Grundlehren der mathematischen Wissenschaften Book ) - Kindle edition by Neukirch, Jürgen, Schmidt, Alexander, Wingberg, Kay.

Download it once and read it on your Kindle device, PC, phones or tablets.5/5(1). Cohomology of Number Fields. Authors: Neukirch, Jürgen, Schmidt, Alexander, Wingberg, Kay Free Preview. Main Cohomology of Number Fields.

Cohomology of Number Fields There are many goodies here. it is an indispensable book for anyone working in number theory. Neukirch, Schmidt, and Wingberg have, in fact, produced authoritative, complete, careful, and sure to be a reliable reference for many years." (Fernando Q. Gouvêa, MathDL.

Cohomology of Number Fields. Authors (view affiliations) Jürgen Neukirch; Alexander Schmidt; Kay Wingberg Cohomology of Global Fields. Jürgen Neukirch, Alexander Schmidt, Kay Wingberg Galois group Galois groups algebra algebraic number field algebraic number fields algebraic number theory arithmetic cohomology cohomology theory finite.

Cohomology of number fields by Jürgen Neukirch, Alexander Schmidt, Kay Wingberg,Springer edition, paperback. Cohomology of Number Fields By JÃ¼rgen Neukirch, Alexander Schmidt, Kay Wingberg Publisher: Sp rin ger | Pages | ISBN: | DJVU | 8 MB Galois modules over local and global fields form the main subject of this monograph, which can serve both as a textbook for students, and as a reference book for the working mathematician, on.

图书Cohomology of Number Fields 介绍、书评、论坛及推荐. Review. From the reviews of the second edition: "The publication of a second edition gives me a chance to emphasize what an important book it is. the book a necessary part of the number theorist’s library. Cohomology of Number Fields Suitable for students, as well as for the working mathematicians on cohomological topics in number theory, this book provides algebraic background: Cohomology of profinite groups, duality groups, free products, and homotopy theory of modules, with sections on spectral sequences and on Tate Cohomology of profinite groups.

cohomology associated to a Grothendieck topos is sufﬁciently covered in the literature (see [5], [], []) and, in any case, it is an easy exercise (at least in dimension 1) to translate between the Galois and the etale languages. 图书Cohomology of Number Fields 介绍、书评、论坛及推荐.

and as a reference book for the working mathematician, on cohomological topics in number theory. The first part provides the necessary algebraic background. The arithmetic part deals with Galois groups of local and global fields: local Tate duality, the structure of the.

Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global : Springer International Publishing.

Cohomology of Number Fields. Galois modules over local and global fields form the main subject of this monograph, which can serve both as a textbook for students, and as a reference book for the working mathematician, on cohomological topics in number theory.

Cohomology of Number Fields, second edition Authors: Jürgen Neukirch, Alexander Schmidt, Kay Wingberg Title: Cohomology of Number Fields, Sec. Ed., print. () Pages: Springer Grundlehren der mathematischen Wissenschaften Bd. A pdf-file of the book, free for non-commercial use, can be downloaded here.

ISBN: OCLC Number: Description: xv, pages ; 24 cm: Contents: Algebraic Theory --Ch. Cohomology of Profinite Groups --Ch. OCLC Number: Description: xv, pages: illustrations ; 24 cm: Contents: Part I Algebraic Theory: Cohomology of Profinite Groups.- Some Homological Algebra.- Duality Properties of Profinite Groups.- Free Products of Profinite Groups.- Iwasawa Modules.- Part II Arithmetic Theory: Galois Cohomology.- Cohomology of Local Fields 4.

Relation to motivic cohomology; p 5. K_3 of a field; p 6. Global fields of finite characteristic; p 7. Local fields; p 8. Number fields at primes where cd=2; p 9. Real number fields at the prime 2; p 10 The K-theory of Z; p Galois cohomology of algebraic number fields Klaus Haberland, Helmut Koch, Thomas Zink Deutscher Verlag der Wissenschaften, - Mathematics - pages.

It begins with the structure theory of local fields, develops group cohomology from scratch, and then proves the main theorem of local class field theory. Unfortunately, this book does not do the work of plainly laying bare its main threads, so requires some patience for self-study.

Neukirch wrote three books on class field theory, algebraic number theory, and the cohomology of number fields: Neukirch, Jürgen (). Class Field mater: University of Bonn. The Galois cohomology groups are then obtained by taking the cohomology of this cochain complex, i.e.

Note: We have adopted here the notation of the book Cohomology of Number Fields by Jurgen Neukirch, Alexander Schmidt, and Kay Wingberg.Proves the duality theorems in Galois, étale, and flat cohomology that have come to play an increasingly important role in number theory and arithmetic geometry, Second corrected TeXed edition (paperback).

Booksurge Publishing, +viii pages, ISBN X Available from bookstores worldwide. List price 24 USD. An online bookstore.Some familiarity with the basic objects of algebra, namely, rings, modules, fields, and so on, as usually covered in advanced undergraduate or beginning graduate courses.

(Topics in) Algebraic Geometry These chapters discuss a few more advanced topics. They can be read in almost any order, except that some assume the first.