T�tulo: Conjectures in Arithmetic Algebraic Geometry: A Survey (Aspects of Mathematics)
Editor: Vieweg+Teubner Verlag
Fecha de publicaci�n: 2013
Idioma: Ingl�s
ISBN 10: 366309507X
ISBN 13: 9783663095071
Encuadernaci�n: Encuadernaci�n de tapa blanda
Edici�n: 2� Edici�n
Estado: New

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Sinopsis

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.

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Dr. Wilfried Hulsbergen is teaching at the KMA, Breda,Niederlande.

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