On p-adic L-series, p-adic cohomology and class field theory

Abstract

Abstract We establish several close links between the Galois structures of a range of arithmetic modules including certain natural families of ray class groups, the values at strictly positive integers of p-adic Artin L-series, the Shafarevich–Weil Theorem and the conjectural surjectivity of certain norm maps in cyclotomic ℤ p {\mathbb{Z}_{p}} -extensions. Non-commutative Iwasawa theory and the theory of organising matrices play a key role in our approach.