In an oscillator where positive feedback is provided through a capacitor in series with a crystal, that type of oscillator is a:

A Pierce oscillator is a popular crystal oscillator design heavily utilized in digital circuits and radio transmitters. It derives its feedback using a capacitor in series with a quartz crystal, which acts as a highly stable resonant circuit in the feedback path. The Pierce design is essentially a series-resonant variation of the Colpitts oscillator, but it specifically features the crystal in the feedback path between the output and input of the amplifying element. Distractors like Hartley and Colpitts rely primarily on tapped inductors or split capacitors for their LC tank circuits, while the Franklin uses extremely light coupling with capacitors to dual amplifier stages.