Abstract: The period-index problem studies the relationship between the period and the index of classes in the Brauer group. Following Kato, we may view H^i(F, \mu_l^{\otimes i-1} ) as a higher degree analogue of Brauer groups and ask a similar question. In this talk, I will report my work on showing such a period-index bound over Hensel semi-global fields, i.e., function fields of curves over excellent henselian discretely valued fields, using the patching technique, which generalizes a recent work by Harbater-Hartmann-Krashen.