Abstract
We present three approaches to define the higher etale regulator maps Φr,net : Hret(X,Z(n)) → HrD(X,Z(n)) for regular arithmetic schemes. The first two approaches construct the maps on the cohomology level, while the third construction provides a morphism of complexes of sheaves on the etale site, along with a technical twist that one needs to replace the Deligne-Beilinson cohomology by the analytic Deligne cohomology inspired by the work of Kerr, Lewis, and Muller-Stach. A vanishing statement of infinite divisible torsions under Φr,net is established for r > 2n + 1.
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