Projectivity of the Witt vector affine Grassmannian
Abstract
We prove that the Witt vector affine Grassmannian, which parametrizes W(k)-lattices in W(k)[1/p]n for a perfect field k of charactristic p, is representable by an ind-(perfect scheme) over k. This improves on previous results of Zhu by constructing a natural ample line bundle. Along the way, we establish various foundational results on perfect schemes, notably h-descent results for vector bundles.
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