The Regulators Of Beilinson And Borel
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The Regulators Of Beilinson And Borel
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Author : José Ignacio Burgos Gil
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
The Regulators Of Beilinson And Borel written by José Ignacio Burgos Gil and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Regulators (Mathematics). categories.
This book contains a complete proof of the fact that Borel's regulator map is twice Beilinson's regulator map. The strategy of the proof follows the argument sketched in Beilinson's original paper and relies on very similar descriptions of the Chern-Weil morphisms and the van Est isomorphism. The book has two different parts. The first one reviews the material from algebraic topology and Lie group theory needed for the comparison theorem. Topics such as simplicial objects, Hopfalgebras, characteristic classes, the Weil algebra, Bott's Periodicity theorem, Lie algebra cohomology, continuous group cohomology and the van Est Theorem are discussed. The second part contains the comparison theorem and the specific material needed in its proof, such as explicit descriptions of theChern-Weil morphism and the van Est isomorphisms, a discussion about small cosimplicial algebras, and a comparison of different definitions of Borel's regulator.
Beilinson S Conjectures On Special Values Of L Functions
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Author : M. Rapoport
language : en
Publisher: Academic Press
Release Date : 2014-07-14
Beilinson S Conjectures On Special Values Of L Functions written by M. Rapoport and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
Beilinson's Conjectures on Special Values of L-Functions deals with Alexander Beilinson's conjectures on special values of L-functions. Topics covered range from Pierre Deligne's conjecture on critical values of L-functions to the Deligne-Beilinson cohomology, along with the Beilinson conjecture for algebraic number fields and Riemann-Roch theorem. Beilinson's regulators are also compared with those of Émile Borel. Comprised of 10 chapters, this volume begins with an introduction to the Beilinson conjectures and the theory of Chern classes from higher k-theory. The "simplest" example of an L-function is presented, the Riemann zeta function. The discussion then turns to Deligne's conjecture on critical values of L-functions and its connection to Beilinson's version. Subsequent chapters focus on the Deligne-Beilinson cohomology; ?-rings and Adams operations in algebraic k-theory; Beilinson conjectures for elliptic curves with complex multiplication; and Beilinson's theorem on modular curves. The book concludes by reviewing the definition and properties of Deligne homology, as well as Hodge-D-conjecture. This monograph should be of considerable interest to researchers and graduate students who want to gain a better understanding of Beilinson's conjectures on special values of L-functions.
Handbook Of K Theory
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Author : Eric Friedlander
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-18
Handbook Of K Theory written by Eric Friedlander and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-18 with Mathematics categories.
This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.
Regulators In Analysis Geometry And Number Theory
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Author : Alexander Reznikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Regulators In Analysis Geometry And Number Theory written by Alexander Reznikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is an outgrowth of the Workshop on "Regulators in Analysis, Geom etry and Number Theory" held at the Edmund Landau Center for Research in Mathematical Analysis of The Hebrew University of Jerusalem in 1996. During the preparation and the holding of the workshop we were greatly helped by the director of the Landau Center: Lior Tsafriri during the time of the planning of the conference, and Hershel Farkas during the meeting itself. Organizing and running this workshop was a true pleasure, thanks to the expert technical help provided by the Landau Center in general, and by its secretary Simcha Kojman in particular. We would like to express our hearty thanks to all of them. However, the articles assembled in the present volume do not represent the proceedings of this workshop; neither could all contributors to the book make it to the meeting, nor do the contributions herein necessarily reflect talks given in Jerusalem. In the introduction, we outline our view of the theory to which this volume intends to contribute. The crucial objective of the present volume is to bring together concepts, methods, and results from analysis, differential as well as algebraic geometry, and number theory in order to work towards a deeper and more comprehensive understanding of regulators and secondary invariants. Our thanks go to all the participants of the workshop and authors of this volume. May the readers of this book enjoy and profit from the combination of mathematical ideas here documented.
Conjectures In Arithmetic Algebraic Geometry
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Author : Wilfred W. J. Hulsbergen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Conjectures In Arithmetic Algebraic Geometry written by Wilfred W. J. Hulsbergen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Technology & Engineering categories.
In the early 1980's, stimulated by work of Bloch and Deligne, Beilinson stated some intriguing conjectures on special values of L-functions of algebraic varieties defined over number fields. Roughly speaking these special values are determinants of higher regulator maps relating the higher algebraic K-groups of the variety to its cohomology. In this respect, higher algebraic K-theory is believed to provide a universal, motivic cohomology theory and the regulator maps are determined by Chern characters from higher algebraic K-theory to any other suitable cohomology theory. Also, Beilinson stated a generalized Hodge conjecture. This book provides an introduction to and a survey of Beilinson's conjectures and an introduction to Jannsen's work with respect to the Hodge and Tate conjectures. It addresses mathematicians with some knowledge of algebraic number theory, elliptic curves and algebraic K-theory.
The Bloch Kato Conjecture For The Riemann Zeta Function
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Author : John Coates
language : en
Publisher: Cambridge University Press
Release Date : 2015-03-13
The Bloch Kato Conjecture For The Riemann Zeta Function written by John Coates and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-13 with Literary Criticism categories.
A graduate-level account of an important recent result concerning the Riemann zeta function.
Motives
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Author : Uwe Jannsen
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Motives written by Uwe Jannsen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Motives were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, to play the role of the missing rational cohomology, and to provide a blueprint for proving Weil's conjectures about the zeta function of a variety over a finite field. Over the last ten years or so, researchers in various areas--Hodge theory, algebraic $K$-theory, polylogarithms, automorphic forms, $L$-functions, $\ell$-adic representations, trigonometric sums, and algebraic cycles--have discovered that an enlarged (and in part conjectural) theory of ``mixed'' motives indicates and explains phenomena appearing in each area. Thus the theory holds the potential of enriching and unifying these areas. This is one of two volumes containing the revised texts of nearly all the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991. A number of related works are also included, making for a total of forty-seven papers, from general introductions to specialized surveys to research papers.
Collected Papers
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Author : Armand Borel
language : en
Publisher: Springer Science & Business Media
Release Date : 1983
Collected Papers written by Armand Borel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
This book collects the papers published by A. Borel from 1983 to 1999. About half of them are research papers, written on his own or in collaboration, on various topics pertaining mainly to algebraic or Lie groups, homogeneous spaces, arithmetic groups (L2-spectrum, automorphic forms, cohomology and covolumes), L2-cohomology of symmetric or locally symmetric spaces, and to the Oppenheim conjecture. Other publications include surveys and personal recollections (of D. Montgomery, Harish-Chandra, and A. Weil), considerations on mathematics in general and several articles of a historical nature: on the School of Mathematics at the Institute for Advanced Study, on N. Bourbaki and on selected aspects of the works of H. Weyl, C. Chevalley, E. Kolchin, J. Leray, and A. Weil. The book concludes with an essay on H. Poincaré and special relativity. Some comments on, and corrections to, a number of papers have also been added.
Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory
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Author : Ulrich Bunke
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory written by Ulrich Bunke and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Education categories.
We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.
The Arithmetic And Geometry Of Algebraic Cycles
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Author : B. Brent Gordon
language : en
Publisher: American Mathematical Soc.
Release Date : 2000-01-01
The Arithmetic And Geometry Of Algebraic Cycles written by B. Brent Gordon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
From the June 1998 Summer School come 20 contributions that explore algebraic cycles (a subfield of algebraic geometry) from a variety of perspectives. The papers have been organized into sections on cohomological methods, Chow groups and motives, and arithmetic methods. Some specific topics include logarithmic Hodge structures and classifying spaces; Bloch's conjecture and the K-theory of projective surfaces; and torsion zero-cycles and the Abel-Jacobi map over the real numbers.