A turbine stator, having multiple stator blades or stator blade segments each of multiple stator blades, wherein each stator blade or each stator blade segment comprises a first shroud and a second shroud, which are formed at ends of a blade leaf of the respective stator blade or of the respective stator blade segment radially located opposite one another, having a first carrier for the stator blades or stator blade segments, wherein each stator blade or each stator blade segment is fastened or supported on the first carrier via a projection of the respective first shroud, having a second carrier for the stator blades or stator blade segments, wherein each stator blade or each stator blade segment is fastened or supported on the second carrier via a projection of the respective second shroud, characterised in that the projection of the first shroud of the respective stator blade or of the respective stator blade segment is inserted into a groove of the first carrier in the radial direction, is supported on an axial surface of the groove of the first carrier via an axial surface portion of crowned contour and fastened and supported in the said groove via a pin extending in the axial direction through the projection of the first shroud with radial moveability in the said groove, in the circumferential direction, wherein seen in the axial direction between the projection of the first shroud of the respective stator blade or of the respective stator blade segment and of the groove of the first carrier there is an axial play, and the projection of the second shroud of the respective stator blade or of the respective stator blade segment is supported on an axial surface of the second carrier via an axial surface portion of crowned contour and, further, is fastened and supported in the circumferential direction and radial direction via a pin extending in the axial direction into the projection of the second shroud and the second carrier. having multiple stator blades or stator blade segments each of multiple stator blades, wherein each stator blade or each stator blade segment comprises a first shroud and a second shroud, which are formed at ends of a blade leaf of the respective stator blade or of the respective stator blade segment radially located opposite one another, having a first carrier for the stator blades or stator blade segments, wherein each stator blade or each stator blade segment is fastened or supported on the first carrier via a projection of the respective first shroud, having a second carrier for the stator blades or stator blade segments, wherein each stator blade or each stator blade segment is fastened or supported on the second carrier via a projection of the respective second shroud, characterised in that the projection of the first shroud of the respective stator blade or of the respective stator blade segment is inserted into a groove of the first carrier in the radial direction, is supported on an axial surface of the groove of the first carrier via an axial surface portion of crowned contour and fastened and supported in the said groove via a pin extending in the axial direction through the projection of the first shroud with radial moveability in the said groove, in the circumferential direction, wherein seen in the axial direction between the projection of the first shroud of the respective stator blade or of the respective stator blade segment and of the groove of the first carrier there is an axial play, and the projection of the second shroud of the respective stator blade or of the respective stator blade segment is supported on an axial surface of the second carrier via an axial surface portion of crowned contour and, further, is fastened and supported in the circumferential direction and radial direction via a pin extending in the axial direction into the projection of the second shroud and the second carrier.