On Swan conductors for Brauer groups of curves over local fields

For an element $w$ of the Brauer group of a curve over a local field, we define the ``Swan conductor'' $\operatorname{sw}(w)$ of $w$, which measures the wildness of the ramification of $w$. We give a relation between $\operatorname{sw}(w)$ and Swan conductors for Brauer groups of henselian discrete valuation fields defined by Kato.