Projectivity of the Witt vector affine Grassmannian

• 成果类型: Article
• 署名作者: Bhatt, Bhargav; Scholze, Peter
• 署名单位: University of Michigan System; University of Michigan; University of Bonn
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0710-4
• 发表日期: 2017
• 页码: 329-423
• 关键词: loop-groups; VARIETIES; COHOMOLOGY; EXTENSIONS; bundles; SPACES

摘要

We prove that the Witt vector affine Grassmannian, which parametrizes W(k)-lattices in for a perfect field k of characteristic 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.