On Non-Noetherian Iwasawa Theory

2024/01/05 by David Burns, Burns, David, Alexandre Daoud +3
Mathematics · #11R20 #11R23 #11R29 #11R34 #11R58 #11R60 #11R65 #11T30 #13F05 #19F27 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2401.02946

openalex publication_date 2024/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathbbG_m for curves over finite fields.

Related

• Iwasawa Theory for p-torsion Class Group Schemes in Characteristic p
• A noncommutative Weierstrass preparation theorem and applications to Iwasawa theory
• Noncommutative Iwasawa theory arising from Hecke algebras
• Fitting Ideals of Projective Limits of Modules over Non-Noetherian Iwasawa Algebras
• Iwasawa theory of Frobenius-torsion class group schemes