Projectivity of the Witt vector affine Grassmannian
Bhargav Bhatt, Peter Scholze
TL;DR
This paper proves that the Witt vector affine Grassmannian is representable by an ind-perfect scheme over a perfect field, enhancing previous results with new foundational insights and a natural ample line bundle.
Contribution
It establishes the representability of the Witt vector affine Grassmannian as an ind-perfect scheme and introduces foundational results on perfect schemes and vector bundles.
Findings
Witt vector affine Grassmannian is representable by an ind-perfect scheme.
Constructed a natural ample line bundle on the Grassmannian.
Established h-descent results for vector bundles on perfect schemes.
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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