Galois Cohomology

Author: Jean-Pierre Serre
Publisher: Springer Science & Business Media
ISBN: 9783642591419
Release Date: 2013-12-01
Genre: Mathematics

This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.

Class Field Theory

Author: Georges Gras
Publisher: Springer Science & Business Media
ISBN: 9783662113233
Release Date: 2013-11-11
Genre: Mathematics

Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.

Brauer Type Embedding Problems

Author: Arne Ledet
Publisher: American Mathematical Soc.
ISBN: 0821871803
Release Date:
Genre: Mathematics

This monograph is concerned with Galois theoretical embedding problems of so-called Brauer type with a focus on 2-groups and on finding explicit criteria for solvability and explicit constructions of the solutions. Before considering questions of reducing the embedding problems and reformulating the solvability criteria, the author provides the necessary theory of Brauer groups, group cohomology and quadratic forms. The book will be suitable for students seeking an introduction to embedding problems and inverse Galois theory. It will also be a useful reference for researchers in the field.

Galois Theory of p Extensions

Author: Helmut Koch
Publisher: Springer Science & Business Media
ISBN: 9783662049679
Release Date: 2013-03-09
Genre: Mathematics

Helmut Koch's classic is now available in English. Competently translated by Franz Lemmermeyer, it introduces the theory of pro-p groups and their cohomology. The book contains a postscript on the recent development of the field written by H. Koch and F. Lemmermeyer, along with many additional recent references.

Konstruktive Galoistheorie

Author: Bernd H. Matzat
Publisher: Springer-Verlag
ISBN: 9783540479789
Release Date: 2006-12-08
Genre: Mathematics

This volume is based on a lecture course on constructive Galois Theory given in Karlsruhe by the author. The purpose of the course was to introduce students to the methods developed in the past few years for the realisation of finite groups as Galois groups over Q or over abelian number fields. Thus the book is addressed primarily to students with algebraic interests, as seminar material. Specialiists also will find in it a multitude of examples of polynomials with special Galois groups, which can of course also be used for the usual algebra courses.

Brauer Groups Hopf Algebras and Galois Theory

Author: Stefaan Caenepeel
Publisher: Springer Science & Business Media
ISBN: 1402003463
Release Date: 2002-03-31
Genre: Mathematics

This volume is devoted to the Brauer group of a commutative ring and related invariants. Part I presents a new self-contained exposition of the Brauer group of a commutative ring. Included is a systematic development of the theory of Grothendieck topologies and �tale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit. Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra. The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I is made clear. Recent developments are considered and examples are included. The Brauer-Long group of a Hopf algebra over a commutative ring is discussed in Part III. This provides a link between the first two parts of the volume and is the first time this topic has been discussed in a monograph. Audience: Researchers whose work involves group theory. The first two parts, in particular, can be recommended for supplementary, graduate course use.

Octonions Jordan Algebras and Exceptional Groups

Author: Tonny A. Springer
Publisher: Springer Science & Business Media
ISBN: 3540663371
Release Date: 2000-05-16
Genre: Mathematics

The 1963 Göttingen notes of T. A. Springer are well-known in the field but have been unavailable for some time. This book is a translation of those notes, completely updated and revised. The part of the book dealing with the algebraic structures is on a fairly elementary level, presupposing basic results from algebra. In the group-theoretical part use is made of some results from the theory of linear algebraic groups. The book will be useful to mathematicians interested in octonion algebras and Albert algebras, or in exceptional groups. It is suitable for use in a graduate course in algebra.

Formes Automorphes I

Author: Jacques Tilouine
ISBN: STANFORD:36105115114592
Release Date: 2005
Genre: Automorphic forms

This volume is the first of a series of two devoted to automorphic forms from a geometric and arithmetic point of view. They also deal with certain parts of the Langlands program. The themes treated in this volume include /p/-adic modular forms, the local Langlands correspondence for /GL(n)/, the cohomology of Shimura varieties, their reduction modulo /p/, and their stratification by Newton polygons. The book is suitable for graduate students and research mathematicians interested in number theory, algebra, and algebraic geometry.


Author: New Zealand Mathematical Society
ISBN: UOM:39015049358339
Release Date: 1994
Genre: Mathematics

p Adic Automorphic Forms on Shimura Varieties

Author: Haruzo Hida
Publisher: Springer Science & Business Media
ISBN: 9781468493900
Release Date: 2012-12-06
Genre: Mathematics

In the early years of the 1980s, while I was visiting the Institute for Ad vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo a prime among elliptic modular forms, that an automorphic L-function of a given algebraic group G should have a canon ical p-adic counterpart of several variables. I immediately decided to find out the reason behind this phenomenon and to develop the theory of ordinary p-adic automorphic forms, allocating 10 to 15 years from that point, putting off the intended arithmetic study of Shimura varieties via L-functions and Eisenstein series (for which I visited lAS). Although it took more than 15 years, we now know (at least conjecturally) the exact number of variables for a given G, and it has been shown that this is a universal phenomenon valid for holomorphic automorphic forms on Shimura varieties and also for more general (nonholomorphic) cohomological automorphic forms on automorphic manifolds (in a markedly different way). When I was asked to give a series of lectures in the Automorphic Semester in the year 2000 at the Emile Borel Center (Centre Emile Borel) at the Poincare Institute in Paris, I chose to give an exposition of the theory of p-adic (ordinary) families of such automorphic forms p-adic analytically de pending on their weights, and this book is the outgrowth of the lectures given there.

Algebraic Patching

Author: Moshe Jarden
Publisher: Springer Science & Business Media
ISBN: 3642151280
Release Date: 2011-01-03
Genre: Mathematics

Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields". Among others, it leads to the solution of two central results in "Field Arithmetic": (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$.