Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On natural complexes in Iwasawa theory

Antonio Mejías Gil, Andreas Nickel

Abstract

We consider two natural complexes that appear in recent formulations of equivariant Iwasawa main conjectures for extensions of not necessarily totally real fields. We show that both complexes are isomorphic in the derived category of Iwasawa modules if the weak Leopoldt conjecture holds for the relevant $\mathbb{Z}_p$-extension.

On natural complexes in Iwasawa theory

Abstract

We consider two natural complexes that appear in recent formulations of equivariant Iwasawa main conjectures for extensions of not necessarily totally real fields. We show that both complexes are isomorphic in the derived category of Iwasawa modules if the weak Leopoldt conjecture holds for the relevant -extension.
Paper Structure (5 sections, 4 theorems, 34 equations)

This paper contains 5 sections, 4 theorems, 34 equations.

Table of Contents

  1. Construction of the main complex
  2. Setup and notation
  3. Local and global complexes
  4. The main complex
  5. The complex of Burns, Kurihara and Sano

Key Result

Lemma 1.2

Using the above notation the following hold:

Theorems & Definitions (12)

  • Definition 1.1
  • Lemma 1.2
  • proof
  • Proposition 1.3
  • proof
  • Remark 1.4
  • Definition 2.1
  • Proposition 2.2
  • proof
  • Remark 2.3
  • ...and 2 more