A b-divisor on a normal variety 
is a compatible assignment of a Weil
divisor to every proper birational model of 
. Compatibility means that pushforward under a morphism between
models gives the assigned divisor on the lower model. The assigned divisor on a model
is its trace. A rational b-divisor is b-
-Cartier when one rational Cartier trace determines all higher
traces by pullback, and b-nef when that determining trace is nef.
For example, pullbacks of a Cartier divisor on 
define a b-Cartier b-divisor. In a canonical bundle formula, the moduli part
is naturally a rational b-divisor. A bounded Cartier denominator requires one common
multiple of the determining trace to be Cartier, rather than merely a bound on selected
visible coefficients.
