A structure theorem for subgroups of GL_n over complete local\n Noetherian rings with large residual image

2013/04/03 by Jayanta Manoharmayum, Manoharmayum, Jayanta · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1304.1196

Abstract

Given a complete local Noetherian ring (A, m_A) with finite residue field\nand a subfield pmbk of A/ m_A, we show that every closed subgroup G of\nGL_n(A) such that G mod m_A\⊇ SL_n( pmbk) contains a conjugate\nof SL_n(W( pmbk)_A) under some small restrictions on pmbk. Here\nW( pmbk)_A is the closed subring of A generated by the Teichm "uller\nlifts of elements of the subfield pmbk.\n

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