Arithmetic Duality Theorems
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Author | : J. S. Milne |
Publisher | : |
Total Pages | : 440 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : |
Download Arithmetic Duality Theorems Book in PDF, Epub and Kindle
Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.
Author | : Peter D. T. A. Elliott |
Publisher | : Cambridge University Press |
Total Pages | : 368 |
Release | : 1997-02-13 |
Genre | : Mathematics |
ISBN | : 0521560888 |
Download Duality in Analytic Number Theory Book in PDF, Epub and Kindle
Deals with analytic number theory; many new results.
Author | : David Harari |
Publisher | : Springer Nature |
Total Pages | : 336 |
Release | : 2020-06-24 |
Genre | : Mathematics |
ISBN | : 3030439011 |
Download Galois Cohomology and Class Field Theory Book in PDF, Epub and Kindle
This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. 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 fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.
Author | : L. McLinden |
Publisher | : |
Total Pages | : 6 |
Release | : 1975 |
Genre | : Duality theory (Mathematics) |
ISBN | : |
Download Duality Theorems and Theorems of the Alternative Book in PDF, Epub and Kindle
It is shown, in a completely general setting, that a theorem of the alternative is logically equivalent to a duality theorem linking two constrained optimization problems.
Author | : Douglas C. Ravenel |
Publisher | : Princeton University Press |
Total Pages | : 228 |
Release | : 1992-11-08 |
Genre | : Mathematics |
ISBN | : 9780691025728 |
Download Nilpotence and Periodicity in Stable Homotopy Theory Book in PDF, Epub and Kindle
Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Author | : Peter D. T. A. Elliott |
Publisher | : Cambridge University Press |
Total Pages | : 362 |
Release | : 1997-02-13 |
Genre | : Mathematics |
ISBN | : 1316582590 |
Download Duality in Analytic Number Theory Book in PDF, Epub and Kindle
In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, structured in chains about individual topics.
Author | : Stephen S. Shatz |
Publisher | : Princeton University Press |
Total Pages | : 264 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400881854 |
Download Profinite Groups, Arithmetic, and Geometry. (AM-67), Volume 67 Book in PDF, Epub and Kindle
In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a treatment of duality. His objective is to present effectively that body of material upon which all modern research in Diophantine geometry and higher arithmetic is based, and to do so in a manner that emphasizes the many interesting lines of inquiry leading from these foundations.
Author | : Miles Reid |
Publisher | : Cambridge University Press |
Total Pages | : 312 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9780521545181 |
Download Number Theory and Algebraic Geometry Book in PDF, Epub and Kindle
This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.
Author | : Jean-Pierre Serre |
Publisher | : Springer Science & Business Media |
Total Pages | : 211 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461210356 |
Download Algebraic Groups and Class Fields Book in PDF, Epub and Kindle
Translation of the French Edition
Author | : David Mumford |
Publisher | : Debolsillo |
Total Pages | : 0 |
Release | : 2008 |
Genre | : Abelian varieties |
ISBN | : 9788185931869 |
Download Abelian Varieties Book in PDF, Epub and Kindle
This is a reprinting of the revised second edition (1974) of David Mumford's classic 1970 book. It gives a systematic account of the basic results about abelian varieties. It includes expositions of analytic methods applicable over the ground field of complex numbers, as well as of scheme-theoretic methods used to deal with inseparable isogenies when the ground field has positive characteristic. A self-contained proof of the existence of the dual abelian variety is given. The structure of the ring of endomorphisms of an abelian variety is discussed. These are appendices on Tate's theorem on endomorphisms of abelian varieties over finite fields (by C. P. Ramanujam) and on the Mordell-Weil theorem (by Yuri Manin). David Mumford was awarded the 2007 AMS Steele Prize for Mathematical Exposition. According to the citation: ``Abelian Varieties ... remains the definitive account of the subject ... the classical theory is beautifully intertwined with the modern theory, in a way which sharply illuminates both ... [It] will remain for the foreseeable future a classic to which the reader returns over and over.''