On Swan conductors for Brauer groups of curves over local fields

Abstract

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