How to center Pivot/Gizmo to object in Object Mode?

title.

i added a cylinder, moved it in edit mode, switched to object mode to duplicate and the stoopid gizmo is where i originally created the object.

Is there a coordinate system in blender? I would like to keep it at the local coordinate system so that i can move it on the same, slanted axis.

You moved it in edit mode, that set the geometry away from the pivot center. Select the object and in Object mode, see the Origin button in the tool bar - press that, and select Origin to Geometry. When moving geo in Edit mode, the center stays put.

thanks for the help Craig.