In mathematics, especially in algebraic geometry, the Beilinson regulator is the Chern class map from algebraic K-theory to Deligne cohomology:
Here, X is a complex smooth projective variety, for example. It is named after Alexander Beilinson. The Beilinson regulator features in Beilinson's conjecture on special values of L-functions.
The Dirichlet regulator map (used in the proof of Dirichlet's unit theorem) for the ring of integers
is a particular case of the Beilinson regulator. (As usual,