Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On Non-Noetherian Iwasawa Theory

David Burns, Alexandre Daoud, Dingli Liang

Abstract

We prove a general structure theorem for finitely presented torsion modules over a class of commutative rings that need not be Noetherian. As a first application, we then use this result to study the Weil- étale cohomology groups of $\mathbb{G}_m$ for curves over finite fields.

On Non-Noetherian Iwasawa Theory

Abstract

We prove a general structure theorem for finitely presented torsion modules over a class of commutative rings that need not be Noetherian. As a first application, we then use this result to study the Weil- étale cohomology groups of for curves over finite fields.
Paper Structure (14 sections, 8 theorems, 57 equations)

This paper contains 14 sections, 8 theorems, 57 equations.

Table of Contents

  1. Introduction
  2. Structure theories over non-Noetherian rings
  3. Finitely presented modules
  4. Generalised characteristic ideals
  5. Inverse limit rings
  6. The general case
  7. The compact case
  8. Weil-étale cohomology for curves over finite fields
  9. Galois groups and power series rings
  10. Structure results
  11. Statement of the main results
  12. Preliminaries on Weil-étale cohomology
  13. The proof of Theorem \ref{['main result']}
  14. The proof of Corollary \ref{['fg cor']}

Key Result

Theorem 2.3

Let $M$ be a finitely presented $A$-module with property (P$_1$). Then the following claims are valid.

Theorems & Definitions (22)

  • Definition 2.1
  • Remark 2.2
  • Theorem 2.3
  • proof
  • Definition 2.4
  • Definition 2.6
  • Proposition 2.7
  • proof
  • Lemma 2.8
  • proof
  • ...and 12 more