English

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