Graduated orders over completed group rings and conductor formulæ

Abstract

We study graduated orders over completed group rings of $1$-dimensional admissible $p$-adic Lie groups, and verify the equivariant $p$-adic Artin conjecture for such orders. Following Jacobinski and Plesken, we obtain a formula for the conductor of a graduated order into a self-dual order. We also refine Nickel's central conductor formula by determining a hitherto implicit exponent $r_{\ddot{I}}‡$.

24 pages, v2: minor revisions following referee report, v3: minor revisions following referee report