On the other hand, there is enormous ambiguity about the choice of $M$.
One should remark that the ambiguity alluded to in Remark 3 disappears when talking about an affine field.
When there is no ambiguity we drop the dependence on $B$ and write just $Y_T$ for $Y_{T,B}$.
This also resolves the ambiguity introduced earlier in choosing an order of the lifts of $U$.
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