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Galois Module Structure Of Galois Cohomology
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Book Synopsis Galois Module Structure of Galois Cohomology by : Andrew Schultz
Download or read book Galois Module Structure of Galois Cohomology written by Andrew Schultz and published by . This book was released on 2007 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cohomology groups associated to the absolute Galois group of a field E encode a great deal of information about E, with the groups Hm(GE, mu p) being of classical interest. These groups are linked to the reduced Milnor K-groups KmE/pK mE = kmE by the Bloch-Kato conjecture. Using this conjecture when E/F is a Galois extension of fields with Gal(E/F) ≃ Z/pnZ for some odd prime p, and additionally assuming xi p ∈ E, we study the groups H m(GE, mup) as modules over the group ring Fp [Gal(E/F)]. When E/F embeds in an extension E'/F with Gal(E'/F) ≃ Z/pn+1 Z , we are able to give a highly stratified decomposition of Hm(GE, mup). This allows us to give a decomposition of the cohomology groups of a p-adic extension of fields. In general we are able to give a coarse decomposition of Hm(GE, mu p), showing that many indecomposable types do not appear in Hm(GE, mup). With an additional assumption about the norm map Nnn-1 : kmEn → k mEn-1, we strengthen this coarse decomposition to a highly stratified one.
Book Synopsis Galois Module Structure by : Victor Percy Snaith
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.
Book Synopsis An Introduction to Galois Cohomology and its Applications by : Grégory Berhuy
Download or read book An Introduction to Galois Cohomology and its Applications written by Grégory Berhuy and published by Cambridge University Press. This book was released on 2010-09-09 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first detailed elementary introduction to Galois cohomology and its applications. The introductory section is self-contained and provides the basic results of the theory. Assuming only a minimal background in algebra, the main purpose of this book is to prepare graduate students and researchers for more advanced study.
Book Synopsis Multiplicative Galois Module Structure by : Alfred Weiss
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.
Book Synopsis Galois Module Structure of Étale Cohomology Groups by : Joel Dodge
Download or read book Galois Module Structure of Étale Cohomology Groups written by Joel Dodge and published by . This book was released on 2011 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with proving a refined function field analogue of the Coates-Sinnott conjecture. The theorem we prove identifies precisely the Fitting ideal of a certain étale cohomology group. The techniques employed are directly inspired by recent work of Greither and Popescu in equivariant Iwasawa theory, both for number fields and function fields. They rest on an in-depth study of the Galois module structure of certain naturally defined 1-motives associated to a function field.
Book Synopsis Galois Cohomology by : Jean-Pierre Serre
Download or read book Galois Cohomology written by Jean-Pierre Serre and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Galois Module Structure of De Rham Cohomology for Tame Covers by : Seon-In Kwon
Download or read book Galois Module Structure of De Rham Cohomology for Tame Covers written by Seon-In Kwon and published by . This book was released on 1995 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Galois Module Structure of Algebraic Integers by : A. Fröhlich
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.
Book Synopsis Galois Theory and Cohomology of Commutative Rings by : Stephen Urban Chase
Download or read book Galois Theory and Cohomology of Commutative Rings written by Stephen Urban Chase and published by American Mathematical Soc.. This book was released on 1969 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modular Forms and Galois Cohomology by : Haruzo Hida
Download or read book Modular Forms and Galois Cohomology written by Haruzo Hida and published by Cambridge University Press. This book was released on 2000-06-29 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.
Book Synopsis Algebraic K-Groups as Galois Modules by : Victor P. Snaith
Download or read book Algebraic K-Groups as Galois Modules written by Victor P. Snaith and published by Birkhäuser. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume began as the last part of a one-term graduate course given at the Fields Institute for Research in the Mathematical Sciences in the Autumn of 1993. The course was one of four associated with the 1993-94 Fields Institute programme, which I helped to organise, entitled "Artin L-functions". Published as [132]' the final chapter of the course introduced a manner in which to construct class-group valued invariants from Galois actions on the algebraic K-groups, in dimensions two and three, of number rings. These invariants were inspired by the analogous Chin burg invariants of [34], which correspond to dimensions zero and one. The classical Chinburg invariants measure the Galois structure of classical objects such as units in rings of algebraic integers. However, at the "Galois Module Structure" workshop in February 1994, discussions about my invariant (0,1 (L/ K, 3) in the notation of Chapter 5) after my lecture revealed that a number of other higher-dimensional co homological and motivic invariants of a similar nature were beginning to surface in the work of several authors. Encouraged by this trend and convinced that K-theory is the archetypical motivic cohomology theory, I gratefully took the opportunity of collaboration on computing and generalizing these K-theoretic invariants. These generalizations took several forms - local and global, for example - as I followed part of number theory and the prevalent trends in the "Galois Module Structure" arithmetic geometry.
Book Synopsis Cohomology of Number Fields by : Jürgen Neukirch
Download or read book Cohomology of Number Fields written by Jürgen Neukirch and published by Springer Science & Business Media. This book was released on 2013-09-26 with total page 831 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. In all it is a virtually complete treatment of a vast array of central topics in algebraic number theory. New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields.
Book Synopsis Class Group Relations and Galois Module Structure by : Bart De Smit
Download or read book Class Group Relations and Galois Module Structure written by Bart De Smit and published by . This book was released on 1993 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Galois Cohomology of Elliptic Curves by : John Coates
Download or read book Galois Cohomology of Elliptic Curves written by John Coates and published by Alpha Science International, Limited. This book was released on 2000 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the material presented in four lectures given by J. Coates at the Tata Institute of Fundamental Research. The original notes were modified and expanded in a joint project with R. Sujatha. The book discusses some aspects of the Iwasawa theory of elliptic curves over algebraic fields. Let E be an elliptic curve defined over an algebraic number field F. The fundamental idea of the Iwasawa theory is to study deep arithmetic questions about E/F, via the study of coarser questions about the arithmetic of E over various infinite extensions of F.
Book Synopsis On Continuous Galois Cohomology by : Alicia Norma Sevilla
Download or read book On Continuous Galois Cohomology written by Alicia Norma Sevilla and published by . This book was released on 1980 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Abelian Galois Cohomology of Reductive Groups by : Mikhail Borovoi
Download or read book Abelian Galois Cohomology of Reductive Groups written by Mikhail Borovoi and published by American Mathematical Soc.. This book was released on 1998 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, a new function H 2/ab (K, G) of abelian Galois cohomology is introduced from the category of connected reductive groups G over a field K of characteristic 0 to the category of abelian groups. The abelian Galois cohomology and the abelianization map ab1: H1 (K, G) -- H 2/ab (K, G) are used to give a functorial, almost explicit description of the usual Galois cohomology set H1 (K, G) when K is a number field
Book Synopsis Galois Cohomology of Algebraic Number Fields by : Klaus Haberland
Download or read book Galois Cohomology of Algebraic Number Fields written by Klaus Haberland and published by . This book was released on 1978 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
