I'm approaching to the Beilinson Conjecture and after studying some properties of the Deligne-Beilinson cohomology, I want to understand the regulator maps. But I don't know anything about K-theory and I would like to understand the necessary background. Is there any reference or some reasonable "chain" of references to follow to understand the construction of regulator? Secondly, I would like to clearly understand the relation between this regulator and L-functions. Can someone help me? Thanks you!
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1$\begingroup$ You could begin with examples. For K_2 of curves, see Dokchitser--de Jeu--Zagier, Numerical verification of Beilinson's conjecture for K_2 of hyperelliptic curves. $\endgroup$– François BrunaultApr 1, 2020 at 17:03
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$\begingroup$ Thanks I will see this paper! What about the background in K-theory? What do you suggest to know about it in general for a depth knowledge of this subject (Beilinson conjectures, regulators etc...)? Thanks! $\endgroup$– Matvey TizovskyApr 2, 2020 at 11:37
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1$\begingroup$ Beilinson's conjecture was originally formulated using K-theory, but a more modern approach is to use motivic cohomology (which is the same as long as we work with non-singular varieties and with rational coefficients). So it is not necessary that you learn K-theory (but the motivic approach uses heavy machinery like A^1-homotopy theory). You can find good references on Beilinson's conjectures here: mathoverflow.net/questions/126699/… Personally I like Ramakrishnan's survey "Regulators, algebraic cycles, and values of L-functions" very much. $\endgroup$– François BrunaultApr 3, 2020 at 12:09
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