Borel regulator

Summary

The Borel regulator is a homomorphism from the odd K-groups of the ring of integers of a number field to a real vector space. For $K_1$ it is the logarithmic embedding of units used for the classical regulator of a number field. Borel showed that for $K_{2m-1}$ with $m \ge 2$ its image is a lattice of full rank. The covolume of this lattice is a rational multiple of a special value of the Dedekind zeta function. It is the number field case of the Beilinson regulator.