Good Reduction of Good Filtrations at Places

Abstract

We consider filtered or graded algebras $A$ over a field $K$. Assume that there is a discrete valuation $O_v$ of $K$ with $m_v$ its maximal ideal and $k_v:=O_v/m_v$ its residue field. Let $\Lambda$ be $O_v$-order such that $\Lambda K=A$ and $\bar{\Lambda }:=k_v{\otimes }_{O_v}\Lambda$ the $\Lambda$-reduction of $A$ at the place $K⇝k_v$. Using the filtration of $A$ induced by $\Lambda$ we shall prove that for certain algebras $A$ their properties are related to $\bar{\Lambda }$.

17 pages