Beilinson's Conjectures on Special Values of L-Functions
Title | Beilinson's Conjectures on Special Values of L-Functions PDF eBook |
Author | M. Rapoport |
Publisher | Academic Press |
Pages | 399 |
Release | 2014-07-14 |
Genre | Mathematics |
ISBN | 1483263304 |
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.
Motives
Title | Motives PDF eBook |
Author | Uwe Jannsen |
Publisher | American Mathematical Soc. |
Pages | 766 |
Release | 1994 |
Genre | Mathematics |
ISBN | 0821827979 |
'Motives' were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, and to play the role of the missing rational cohomology. This work contains the texts of the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991.
Arithmetic of L-functions
Title | Arithmetic of L-functions PDF eBook |
Author | Cristian Popescu |
Publisher | American Mathematical Soc. |
Pages | 517 |
Release | |
Genre | Mathematics |
ISBN | 0821886983 |
Conjectures in Arithmetic Algebraic Geometry
Title | Conjectures in Arithmetic Algebraic Geometry PDF eBook |
Author | Wilfred W. J. Hulsbergen |
Publisher | Springer Science & Business Media |
Pages | 247 |
Release | 2013-06-29 |
Genre | Technology & Engineering |
ISBN | 3663095053 |
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.
L-Functions and Arithmetic
Title | L-Functions and Arithmetic PDF eBook |
Author | J. Coates |
Publisher | Cambridge University Press |
Pages | 404 |
Release | 1991-02-22 |
Genre | Mathematics |
ISBN | 0521386195 |
Aimed at presenting nontechnical explanations, all the essays in this collection of papers from the 1989 LMS Durham Symposium on L-functions are the contributions of renowned algebraic number theory specialists.
The Bloch-Kato Conjecture for the Riemann Zeta Function
Title | The Bloch-Kato Conjecture for the Riemann Zeta Function PDF eBook |
Author | John Coates |
Publisher | Cambridge University Press |
Pages | 317 |
Release | 2015-03-13 |
Genre | Mathematics |
ISBN | 1107492963 |
A graduate-level account of an important recent result concerning the Riemann zeta function.
A Survey of the Hodge Conjecture
Title | A Survey of the Hodge Conjecture PDF eBook |
Author | James Dominic Lewis |
Publisher | American Mathematical Soc. |
Pages | 386 |
Release | 1999 |
Genre | Mathematics |
ISBN | 0821805681 |
This book provides an introduction to a topic of central interest in transcendental algebraic geometry: the Hodge conjecture. Consisting of 15 lectures plus addenda and appendices, the volume is based on a series of lectures delivered by Professor Lewis at the Centre de Recherches Mathematiques (CRM). The book is a self-contained presentation, completely devoted to the Hodge conjecture and related topics. It includes many examples, and most results are completely proven or sketched. The motivation behind many of the results and background material is provided. This comprehensive approach to the book gives it a 'user-friendly' style. Readers need not search elsewhere for various results. The book is suitable for use as a text for a topics course in algebraic geometry. It includes an appendix by B. Brent Gordon.