The Iwasawa Algebra Ω_G and Its Dual Artin Coalgebra

2016/10/25 by Zheng Fang, Feng Wei, Fang, Zheng +1
Mathematics · #11R23 #16S34 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA #msc:11R23 #msc:16S34

paper · pdf · doi:10.48550/arxiv.1610.07761

8 pages

arxiv created 2016/10/25 · openalex publication_date 2016/10/25 · arxiv updated 2016/10/26 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

For any compact p-adic Lie group G, the Iwasawa algebra Ω_G over finite field \mathbbF_p is a complete noetherian semilocal algebra. It is shown that Ω_G is the dual algebra of an artinian coalgebra C. We induce a duality between the derived category D^b_fg(_ΩGM) of bounded complexes of left Ω_G-modules with finitely generated cohomology modules and the derived category D^b_qf(^CM) of bounded complexes of left C-comodules with quasi-finite cohomology comodules.

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