2013/03/02 by Ching-Li Chai, Chai, Ching-Li, Christian Kappen +1
Mathematics · #14K15 (Primary) 11S15 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11S15 #msc:14K15
paper · pdf · doi:10.48550/arxiv.1303.0423
arxiv created 2013/03/02 · arxiv updated 2013/03/05
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 1/2 ArK, 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 analytic K-torus T is equal to the value of bArK on the Qp-rational Galois representation X^*(T)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.