On a new type of the l-adic regulator for algebraic number fields

Abstract

For an algebraic number field K such that prime l splits completely in K we define a regulator R(K) that characterize the subgroup of universal norms from the cyclotomic extension of K in the completed group of S-units of K, where S consists of all prime divisors of l. We prove that inequality R(K) not equals 0 follows from the l-adic Schanuel conjecture and holds true for some Abelian extensions of imaginary quadratic fields.