An Al2O3 carrier has a thin-film structure of platinum or a platinum alloy arranged thereon. The carrier and/or the thin-film structure are adapted to reduce mechanical stresses owing to different thermal expansion coefficients. The carrier and/or the thin-film structure include a surface of the carrier in the region of the thin-film structure is smoothed at least in sections to reduce the adhesion and/or a surface of the carrier has an intermediate layer on which the thin-film structure is arranged. The thermal expansion coefficient of the intermediate layer is from 8*10−6/K to 16*10−6/K, in particular from 8.5*10−6/K to 14*10−6/K, and/or the thin-film structure has at least one conductor path that is undular at least in sections, said conductor path extends laterally along the surface of the carrier.