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Author : Martin John Taylor
Publisher :
ISBN 13 :
Total Pages : 162 pages
Book Rating : 4.:/5 (731 download)
Download or read book Galois Module Structure of the Integers of E - Extensions written by Martin John Taylor and published by . This book was released on 1977 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. Fröhlich
Publisher : Springer Science & Business Media
ISBN 13 : 3642688160
Total Pages : 271 pages
Book Rating : 4.6/5 (426 download)
Download or read book Galois Module Structure of Algebraic Integers written by A. Fröhlich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin L-functions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields -in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ("normal integral basis"). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools.
Author : Gove Griffith Elder
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.:/5 (314 download)
Download or read book The Galois Module Structure of the Integers in Wildly Ramified Extensions written by Gove Griffith Elder and published by . This book was released on 1993 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Albrecht Fröhlich
Publisher : Springer
ISBN 13 :
Total Pages : 282 pages
Book Rating : 4.4/5 (91 download)
Download or read book Galois Module Structure of Algebraic Integers written by Albrecht Fröhlich and published by Springer. This book was released on 1983 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Victor Percy Snaith
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871782
Total Pages : 220 pages
Book Rating : 4.8/5 (717 download)
Download or read book Galois Module Structure written by Victor Percy Snaith and published by American Mathematical Soc.. This book was released on 1994-01-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first published graduate course on the Chinburg conjectures, and this book provides the necessary background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. The computation of Hom-descriptions is facilitated by Snaith's Explicit Brauer Induction technique in representation theory. In this way, illustrative special cases of the main results and new examples of the conjectures are proved and amplified by numerous exercises and research problems.
Author : Lindsay N. Childs
Publisher : American Mathematical Soc.
ISBN 13 : 1470465167
Total Pages : 311 pages
Book Rating : 4.4/5 (74 download)
Download or read book Hopf Algebras and Galois Module Theory written by Lindsay N. Childs and published by American Mathematical Soc.. This book was released on 2021-11-10 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
Author : Alfred Weiss
Publisher : American Mathematical Soc.
ISBN 13 : 0821802658
Total Pages : 106 pages
Book Rating : 4.8/5 (218 download)
Download or read book Multiplicative Galois Module Structure written by Alfred Weiss and published by American Mathematical Soc.. This book was released on 1996 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is the result of a short course on the Galois structure of S -units that was given at The Fields Institute in the autumn of 1993. Offering a new angle on an old problem, the main theme is that this structure should be determined by class field theory, in its cohomological form, and by the behaviour of Artin L -functions at s = 0. A proof of this - or even a precise formulation - is still far away, but the available evidence all points in this direction. The work brings together the current evidence that the Galois structure of S -units can be described. This is intended for graduate students and research mathematicians, specifically algebraic number theorists.
Author : Ted Chinburg
Publisher : American Mathematical Soc.
ISBN 13 : 0821824589
Total Pages : 167 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Analytic Theory of Multiplicative Galois Structure written by Ted Chinburg and published by American Mathematical Soc.. This book was released on 1989 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main object of this memoir is to describe and, in some cases, to establish, new systems of congruences for the algebraic parts of the leading terms of the expansions of [italic]L-series at [italic lowercase]s = 0. If these congruences hold, together with a conjecture of Stark which states (roughly) that the ratio of the leading term to the regulator is an algebraic integer, then the main conjecture is true. The greater part of the memoir is devoted to the study of these systems of congruences for certain infinite families of quaternion extensions [italic]N/[italic]K (that is, [capital Greek]Gamma quaternion order 8). It is shown that such extensions can be constructed with specified ramification, and that various unit and class groups are calculable. This permits the verification of the congruences, and the main conjecture can be established for one such family of extensions.
Author : Caiqun Xiao
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (187 download)
Download or read book Galois Module Structure of Elliptic Curves Over Number Fields written by Caiqun Xiao and published by . This book was released on 1997 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wladyslaw Narkiewicz
Publisher : Springer Science & Business Media
ISBN 13 : 3662070014
Total Pages : 712 pages
Book Rating : 4.6/5 (62 download)
Download or read book Elementary and Analytic Theory of Algebraic Numbers written by Wladyslaw Narkiewicz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Author : Cornelius Greither
Publisher : Springer
ISBN 13 : 3540475397
Total Pages : 155 pages
Book Rating : 4.5/5 (44 download)
Download or read book Cyclic Galois Extensions of Commutative Rings written by Cornelius Greither and published by Springer. This book was released on 2006-11-15 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The structure theory of abelian extensions of commutative rings is a subjectwhere commutative algebra and algebraic number theory overlap. This exposition is aimed at readers with some background in either of these two fields. Emphasis is given to the notion of a normal basis, which allows one to view in a well-known conjecture in number theory (Leopoldt's conjecture) from a new angle. Methods to construct certain extensions quite explicitly are also described at length.
Author : Klaus W. Roggenkamp
Publisher : Springer
ISBN 13 : 3540387897
Total Pages : 490 pages
Book Rating : 4.5/5 (43 download)
Download or read book Integral Representations and Applications written by Klaus W. Roggenkamp and published by Springer. This book was released on 2006-11-14 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. J. Scholl
Publisher : Cambridge University Press
ISBN 13 : 0521644194
Total Pages : 506 pages
Book Rating : 4.5/5 (216 download)
Download or read book Galois Representations in Arithmetic Algebraic Geometry written by A. J. Scholl and published by Cambridge University Press. This book was released on 1998-11-26 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.
Author : Jürgen Ritter
Publisher : American Mathematical Soc.
ISBN 13 : 0821829289
Total Pages : 105 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Lifted Root Number Conjecture and Iwasawa Theory written by Jürgen Ritter and published by American Mathematical Soc.. This book was released on 2002 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper concerns the relation between the Lifted Root Number Conjecture, as introduced in [GRW2], and a new equivariant form of Iwasawa theory. A main conjecture of equivariant Iwasawa theory is formulated, and its equivalence to the Lifted Root Number Conjecture is shown subject to the validity of a semi-local version of the Root Number Conjecture, which itself is proved in the case of a tame extension of real abelian fields.
Author : Hyman Bass
Publisher : World Scientific
ISBN 13 : 9814544795
Total Pages : 622 pages
Book Rating : 4.8/5 (145 download)
Download or read book Algebraic K-theory And Its Applications - Proceedings Of The School written by Hyman Bass and published by World Scientific. This book was released on 1999-03-12 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings volume is divided into two parts. The first part consists of lectures given during the first two weeks devoted to a workshop featuring state-of-the-art expositions on 'Overview of Algebraic K-theory' including various constructions, examples, and illustrations from algebra, number theory, algebraic topology, and algebraic/differential geometry; as well as on more concentrated topics involving connections of K-theory with Galois, etale, cyclic, and motivic (co)homologies; values of zeta functions, and Arithmetics of Chow groups and zero cycles. The second part consists of research papers arising from the symposium lectures in the third week.
Author : S. V. Vostokov
Publisher : American Mathematical Soc.
ISBN 13 : 0821832670
Total Pages : 232 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebraic Number Theory and Algebraic Geometry written by S. V. Vostokov and published by American Mathematical Soc.. This book was released on 2002 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: A. N. Parshin is a world-renowned mathematician who has made significant contributions to number theory through the use of algebraic geometry. Articles in this volume present new research and the latest developments in algebraic number theory and algebraic geometry and are dedicated to Parshin's sixtieth birthday. Well-known mathematicians contributed to this volume, including, among others, F. Bogomolov, C. Deninger, and G. Faltings. The book is intended for graduate students andresearch mathematicians interested in number theory, algebra, and algebraic geometry.
Author : K.W. Roggenkamp
Publisher : Birkhäuser
ISBN 13 : 303488611X
Total Pages : 215 pages
Book Rating : 4.0/5 (348 download)
Download or read book Group Rings and Class Groups written by K.W. Roggenkamp and published by Birkhäuser. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the book centers around the isomorphism problem for finite groups; i.e. which properties of the finite group G can be determined by the integral group ring ZZG ? The authors have tried to present the results more or less selfcontained and in as much generality as possible concerning the ring of coefficients. In the first section, the class sum correspondence and some related results are derived. This part is the proof of the subgroup rigidity theorem (Scott - Roggenkamp; Weiss) which says that a finite subgroup of the p-adic integral group ring of a finite p-group is conjugate to a subgroup of the finite group. A counterexample to the conjecture of Zassenhaus that group basis are rationally conjugate, is presented in the semilocal situation (Scott - Roggenkamp). To this end, an extended version of Clifford theory for p-adic integral group rings is presented. Moreover, several examples are given to demonstrate the complexity of the isomorphism problem. The second part of the book is concerned with various aspects of the structure of rings of integers as Galois modules. It begins with a brief overview of major results in the area; thereafter the majority of the text focuses on the use of the theory of Hopf algebras. It begins with a thorough and detailed treatment of the required foundational material and concludes with new and interesting applications to cyclotomic theory and to elliptic curves with complex multiplication. Examples are used throughout both for motivation, and also to illustrate new ideas.
