Dirichlet's Unit Theorem - Higher Regulators

Higher Regulators

A 'higher' regulator refers to a construction for an algebraic K-group with index n > 1 that plays the same role as the classical regulator does for the group of units, which is a group K₁. A theory of such regulators has been in development, with work of Armand Borel and others. Such higher regulators play a role, for example, in the Beilinson conjectures, and are expected to occur in evaluations of certain L-functions at integer values of the argument.