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Non-commutative twisted Euler characteristic

2017/10/11 by Somnath Jha, Sudhanshu Shekhar, Jha, Somnath +1
Mathematics · #11R23 #14H52 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT #msc:11R23 #msc:14H52

paper · pdf · doi:10.48550/arxiv.1710.03985

to appear in Münster Journal of Mathematics

arxiv created 2017/10/11 · openalex publication_date 2017/10/11 · arxiv updated 2017/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that given a finitely generated torsion module M over the Iwasawa algebra \mathbb Zp[[Γ]], where Γ≅ \mathbb Zp, there exists a continuous p-adic character ρ of Γ such that, for the twist M(ρ) of M, the Γn := Γpn Euler characteristic, i.e. χ(Γn, M(ρ)), is finite for every n. We prove a generalization of this result by considering modules over the Iwasawa algebra of a general p-adic Lie group G, instead of Γ. We relate this twisted Euler characteristic to the evaluation of the \it Akashi series at the twist and in turn use it to indicate some application to the Iwasawa theory of elliptic curves. This article is a natural generalization of the result established in [JOZ].

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