Write a balanced half-reaction describing the oxidation of aqueous gold(i) cations to aqueous gold(iii) cations.

Balanced half-reaction: Au⁺(aq) →  Au³⁺(aq) + 2e⁻.
Oxidation reaction is increasing of oxidation number of element, because element or ion lost electrons in chemical reaction.
Gold lost two electrons and change oxidation number from +1 to +3.
Reduction is lowering oxidation number because element gain electrons.