The failure of GCH at a degree of supercompactness

@article{Cody2012TheFO,
  title={The failure of GCH at a degree of supercompactness},
  author={Brent Cody},
  journal={Math. Log. Q.},
  year={2012},
  volume={58},
  pages={83-94}
}
We determine the large cardinal consistency strength of the existence of a λ-supercompact cardinal κ such that GCH fails at λ. Indeed, we show that the existence of a λ-supercompact cardinal κ such that 2 ≥ θ is equiconsistent with the existence of a λ-supercompact cardinal that is also θ-tall. We also prove some basic facts about the large cardinal notion of tallness with closure.