A refinement of the Artin conductor and the base change conductor

For a local field K with positive residue characteristic p, we introduce, in the first part of this paper, a refinement bArK of the classical Artin distribution ArK . It takes values in cyclotomic extensions of Q which are unramified at p, and it bisects ArK in the sense that ArK is equal to the sum of bArK and its conjugate distribution. Compared with 12ArK , the bisection bArK provides a higher resolution on the level of tame ramification. In the second part of this article, we prove that the base change conductor c(T ) of an analyticK-torus T is equal to the value of bArK on the Qp-rational Galois representation X∗(T )⊗Zp Qp that is given by the character module X∗(T ) of T . We hereby generalize a formula for the base change conductor of an algebraic K-torus, and we obtain a formula for the base change conductor of a semiabelian K-variety with potentially ordinary reduction.