Abstract
In this chapter we describe two examples of maps from algebraic K-theory to Deligne-Beilinson cohomology that can be considered as a first motivation for Beilinson’s conjectures. These conjectures are then formulated in such a way that they generalize, at the same time, a conjecture of Deligne on the values of L-functions of motives at so-called critical points. We will state the conjectures only for smooth projective varieties defined over the rational numbers, but it should be observed that almost everything can be formulated for motives over arbitrary number fields, the statements becoming just more complicated.
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Notes
Both authors use different notations for our D3.
It seems that Beilinson has made substantial progress on Zagier’s Main Conjecture.
i.e. motives for absolute Hodge cycles in the language of Chapter 8.
Cf. Chapter 10 for Deligne’s Conjecture for Hecke L-functions
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© 1992 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Hulsbergen, W.W.J. (1992). Regulators, Deligne’s conjecture and Beilinson’s first conjecture. In: Conjectures in Arithmetic Algebraic Geometry. Aspects of Mathematics, vol 18. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-85466-7_6
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DOI: https://doi.org/10.1007/978-3-322-85466-7_6
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-06433-4
Online ISBN: 978-3-322-85466-7
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