The p-adic Coates–Sinnott Conjecture over maximal orders

Abstract

We prove the [Formula: see text]-adic version of the Coates–Sinnott Conjecture for all primes [Formula: see text], without assuming the vanishing of [Formula: see text]-invariants, for finite abelian extensions [Formula: see text] of a totally real number field [Formula: see text], where either the integral group ring [Formula: see text] of the Galois group [Formula: see text] is a maximal order in [Formula: see text] or [Formula: see text] is a CM-field of degree [Formula: see text] with [Formula: see text] odd and [Formula: see text], where the group ring [Formula: see text] is not a maximal order. The only assumption we have to make concerns the prime [Formula: see text], where for non-abelian fields we have to assume the Main Conjecture in Iwasawa theory and the equality of algebraic and analytic [Formula: see text]-invariants.