= Independence of characteristic support from a good module filtration
{title2=$\sqrt{\operatorname{Ann}\operatorname{gr}_FM}=\sqrt{\operatorname{Ann}\operatorname{gr}_GM}$}
Fix the <Bernstein filtration> on the <Weyl algebra>. Two <good filtrations of a module> are bounded shifts of one another: $F_iM\subseteq G_{i+c}M$ and conversely. If an operator of degree $d$ has symbol annihilating $\operatorname{gr}_FM$, its $r$th power lowers the expected filtration degree by $r$. For $r>2c$, comparison of filtrations forces the same power of its symbol to annihilate $\operatorname{gr}_GM$. Reversing the roles gives equality of the radical <annihilator> ideals and hence equality of <support of a module>. The algebra filtration is held fixed; changing between order and Bernstein filtrations need not preserve the same variety.
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