On Universal Norms for $p$-adic Representations in Higher Rank Iwasawa Theory

Abstract

We begin a systematic investigation of universal norms for p-adic representations in higher rank Iwasawa theory. After establishing the basic properties of the module of higher rank universal norms we construct an Iwasawa-theoretic pairing that is relevant to this setting. This allows us, for example, to refine the classical Iwasawa Main Conjecture for cyclotomic fields, and also to give applications to various well-known conjectures in arithmetic concerning Iwasawa invariants and leading terms of L-functions.

On the structure of the module of Euler systems for a $p$-adic representation

“…Moreover, the Euler-Poincaré characteristic of the complex Q⊗ R C E,U,Σ (T ) vanishes. (2) There is a canonical isomorphism H 0 (C E,U,Σ (T )) ∼ = H 1 Σ (O E,U , T * (1)) and a split exact sequence…”