X is a smooth quasi-projective variety over Q.(adsbygoogle = window.adsbygoogle || []).push({});

Beilinson's regulator map is a map from the motivic cohomology H to the Deligne cohomology H_D. Originally the motivic cohomology was defined by Beilinson as an eigenspace of an Adams operation on an algebraic K-group. Bloch (or Levine or someone else) showed the lambda piece of K coincides with Bloch's higher Chow group. Then Voevodsky claims higher Chow group is the same as his motivic cohomology defined by his motivic complex.

My question is is it possible to give explicit formula of Beilinson's regulator map as a morphism between Voevodsky's motivic complex (over a Zariski, etale site) and Deligne complex (over an analytic manifold)? Even for a certain limited case....

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# Beilinson's regulator map

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