Abstract
We consider filtered or graded algebras A over a field K. Assume that there is a discrete valuation Ov of K with mv its maximal ideal and kv:=Ov/mv its residue field. Let Λ be Ov-order such that ΛK=A and \(\overline{\Lambda}:=k_{v}\otimes_{O_{v}}\Lambda\) the Λ-reduction of A at the place \(K\leadsto k_{v}\) . As in many examples of quantized algebras A comes with a specific filtration that reduces well with respect to the valuation filtration defined by Λ on A and the reduction relates to the part of degree zero in the associated graded algebra. Hence several lifting properties fellow from valuation like theory, also for modules with good filtrations.
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Mathematics Subject Classifications (2000)
16W35, 16W70, 16W60, 06B23, 06B25.
Toukaiddine Petit: Author supported by the Scientific Programme NOG of the European Science Foundation.
Freddy Oystaeyen: Acknowledging the EC project Liegrits MCRTN 505078.
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Petit, T., Van Oystaeyen, F. Good Reduction of Good Filtrations at Places. Algebr Represent Theor 9, 201–216 (2006). https://doi.org/10.1007/s10468-005-8761-z
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DOI: https://doi.org/10.1007/s10468-005-8761-z