We say a principal pair $(X,\mathcal{I})$ where $X=Spec(A)$ is affine scheme and $\mathcal{I}=\tilde{I}$ where $I\subset A$ is a principal ideal generated by $\pi$ wich is a non zero divisor.
For a principal pair $(X,\mathcal{I})$ and $f:Spec(B)\rightarrow X$ a finite type morphism, Temkin defines in 3.2.5 http://www.math.huji.ac.il/~temkin/papers/Excellent_Desingularization.pdf
the conductor of $r(f)$ to be the minimal integer $r$ such that $I^{r}\subset H_{B/A}$ where $H_{B/A}$ is the Gabber- Ramero ideal (cf. 3.2.2).
Now we consider a family $Y\rightarrow\mathbb{A}^{1}\times_{k}X $where $X$ is a smooth projective curve over an algebraically field $k$.
At each closed point $a\in\mathbb{A}^{1}$ we then have a "cover" $f_{a}:Y_{a}\rightarrow X$ and so at each closed point $x\in X$, we have a local conductor $r(f_{a},x)$.
My question is do we have that $a\mapsto \sum\limits_{x\in X}r(f_{a},x)$ is upper semi-continuous?
