Projectivity of the Witt vector affine Grassmannian
By B. Bhatt, Peter Scholze. Inventiones Mathematicae, 2015
243 citations recorded by the source corpus.
We prove that the Witt vector affine Grassmannian, which parametrizes W(k)-lattices in $$W(k)[\frac{1}{p}]^n$$W(k)[1p]n 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fc5fcf508d623bdacdaee103cbbfe88dbd593386
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In Geometry and Topology
- B. Bhatt
- A. Mathew
- Laurent Fargues
- Peter Scholze
- A. Beilinson
- Wiesława Nizioł
- Arpon Raksit
- Ruochuan Liu
In Mathematical Physics
- B. Bhatt
- A. Mathew
- Peter Scholze
- Laurent Fargues
- A. Beilinson
- Wiesława Nizioł
- Arpon Raksit
- Ruochuan Liu
Citations in the corpus
- Geometrization of the local Langlands correspondence: an overview (2016, background): “If G is unramified there is an object sitting over Spa(OE) whose special fiber over Fq is the Witt vectors affine Grassmanian as defined by Zhu ([32], [29]) and whose generic fiber over E is the BdR-affine Grassmanian.”
- The arc-topology (2018, background): “The starting point for us is the so-called v-topology or universally subtrusive topology, studied by [39, 4]:”