Graduated orders over completed group rings and conductor formulæ

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_χ.