Hey David,
we carried one half rope, and doubled it (=30 m). We simulclimbed most of the route, but for some sections we set up a belay. There are two short exposed sections on the ridge, and then the "crux" (alpinedave gives it a 5.5., was icy for us, but well protectable with runners), which leads to the false summit. We brought a set of nuts, but didn't use it. There are many little horns for runners. Hope that helps. And yes, do bring crampons for the approach to the notch.