Projectivity of the Witt vector affine Grassmannian
Algebraic Geometry
2017-02-22 v3 Number Theory
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.
Keywords
Cite
@article{arxiv.1507.06490,
title = {Projectivity of the Witt vector affine Grassmannian},
author = {Bhargav Bhatt and Peter Scholze},
journal= {arXiv preprint arXiv:1507.06490},
year = {2017}
}
Comments
v3: Revised and final version