Grassmannians of absolute Banach-Colmez Spaces
Abstract
We introduce Grassmannians of absolute Banach--Colmez spaces and prove the k-Grassmannian is perfectoid if and only if the space has slope < 1/k. For d=1, this proves a conjecture of Hansen--Mann. The key ingredient is a Plücker morphism, which realizes the k-Grassmannian of a slope d/n space as a Zariski closed subspace of the projectivization of a slope kd/n space. We also introduce a general method to construct invariant elements in perfectoid Tate--Huber pairs, and use this to prove absolute Banach--Colmez spaces of slope <1 have perfectoid projectivizations. As applications, we establish vanishing bounds for Scholze's mod p Jacquet--Langlands functor on parabolic inductions, and also prove its vanishing in the top degree on every infinite-dimensional non-supersingular irreducible representation.
Related
- Empirical Bernstein in smooth Banach spaces
- Uniform Embeddings of Banach Space Spheres into Hilbert Spaces and Property (H)
- Improved Bounds For The Lipschitz Retraction Constant In Classical Banach Spaces
- Compactness in Combinatorial Banach Spaces and Beyond
- Spectral theorem for compact self-adjoint operators on smooth Banach spaces
BibTeX
@misc{yi2026grassmannians,
title = {{Grassmannians of absolute Banach-Colmez Spaces}},
author = {Zecheng Yi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42110},
eprint = {2610.42110},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42110},
}
RIS
TY - UNPB
TI - Grassmannians of absolute Banach-Colmez Spaces
AU - Zecheng Yi
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42110
UR - https://arxiv.org/abs/2610.42110
AB - We introduce Grassmannians of absolute Banach--Colmez spaces and prove the k-Grassmannian is perfectoid if and only if the space has slope < 1/k. For d=1, this proves a conjecture of Hansen--Mann. The key ingredient is a Plücker morphism, which realizes the k-Grassmannian of a slope d/n space as a Zariski closed subspace of the projectivization of a slope kd/n space. We also introduce a general method to construct invariant elements in perfectoid Tate--Huber pairs, and use this to prove absolute Banach--Colmez spaces of slope <1 have perfectoid projectivizations. As applications, we establish vanishing bounds for Scholze's mod p Jacquet--Langlands functor on parabolic inductions, and also prove its vanishing in the top degree on every infinite-dimensional non-supersingular irreducible representation.
ER -