Conjectures in Arithmetic Algebraic Geometry A Survey 

Author:
 Hulsbergen, Wilfred W. J. 
Series title:  Aspects of Mathematics Ser. 
ISBN:  9783663095071 
Publication Date:  Oct 2013 
Publisher:  Vieweg Verlag, Friedr, & Sohn Verlagsgesellschaft mbH

Book Format:  Paperback 
List Price:  USD $99.00 
Book Description:

In the early 1980's, stimulated by work of Bloch and Deligne, Beilinson stated some intriguing conjectures on special values of Lfunctions of algebraic varieties defined over number fields. Roughly speaking these special values are determinants of higher regulator maps relating the higher algebraic Kgroups of the variety to its cohomology. In this respect, higher algebraic Ktheory is believed to provide a universal, motivic cohomology theory and the regulator maps are determined by...
More DescriptionIn the early 1980's, stimulated by work of Bloch and Deligne, Beilinson stated some intriguing conjectures on special values of Lfunctions of algebraic varieties defined over number fields. Roughly speaking these special values are determinants of higher regulator maps relating the higher algebraic Kgroups of the variety to its cohomology. In this respect, higher algebraic Ktheory is believed to provide a universal, motivic cohomology theory and the regulator maps are determined by Chern characters from higher algebraic Ktheory 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 Ktheory.