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

Jayanta Manoharmayum

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

Rings and Algebras 2013-07-15 v2 Number Theory

Authors: Jayanta Manoharmayum

Abstract

Given a complete local Noetherian ring $(A,\m_A)$ with finite residue field and a subfield $\pmb{k}$ of $A/\m_A$ , we show that every closed subgroup $G$ of $GL_n(A)$ such that $G\mod{\m_A}\supseteq SL_n(\pmb{k})$ contains a conjugate of $SL_n(W(\pmb{k})_A)$ under some small restrictions on $\pmb{k}$ . Here $W(\pmb{k})_A$ is the closed subring of $A$ generated by the Teichm\"{u}ller lifts of elements of the subfield $\pmb{k}$ .

Keywords

general linear group complete local noetherian rings subgroups residual image teichmüller lifts special linear group structure theorem

Cite

@article{arxiv.1304.1196,
  title  = {A structure theorem for subgroups of $GL_n$ over complete local Noetherian rings with large residual image},
  author = {Jayanta Manoharmayum},
  journal= {arXiv preprint arXiv:1304.1196},
  year   = {2013}
}

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Revised and updated

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

Abstract

Keywords

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