PreprintarXiv licencearXiv
Steinness of the Basic GLn Local Shimura Tower in Odd Rank
Abstract
We prove Steinness over breveQp for the basic local Shimura tower attached to G=GLn, μ=(1,1,0n−2), with basic Newton slope 2/n, for every odd n≥3, at every finite level and for every prime p. The proof proceeds by constructing global analytic functions from the crystalline period map, proving compactness of their sublevel sets via a perfectoid normalization of Tate lattices, and showing that the resulting function map to affine space is finite. The key geometric inputs are the Fargues--Fontaine realization of the universal cover, a normalized determinant on the rank-two locus, and an integral PEL realization over W(F̅p) used to produce bounded global Hodge generators. The integral constructions include the prime p=2.
Related
- Basic Theory of Tower Systems
- Deformation families of open Calabi-Yau manifolds and Steinness
- On the algebraicity of non-abelian Noether-Lefschetz loci of rank-two real local systems
- Functional Regression with Reconstructed Curves: Local Rank Stability and Optimized Confidence Certificates
- Finite Local Rings Free of Rank Three over Zpn: Radical Filtrations, Matrix Models, and the Frobenius Property
BibTeX
@misc{yang2026steinness,
title = {{Steinness of the Basic $\mathrmGL_n$ Local Shimura Tower in Odd Rank}},
author = {Jiawei Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22921},
eprint = {2609.22921},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22921},
}
RIS
TY - UNPB
TI - Steinness of the Basic GL_n Local Shimura Tower in Odd Rank
AU - Jiawei Yang
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22921
UR - https://arxiv.org/abs/2609.22921
AB - We prove Steinness over breveQ_p for the basic local Shimura tower attached to G=GL_n, μ=(1,1,0^n−2), with basic Newton slope 2/n, for every odd n≥3, at every finite level and for every prime p. The proof proceeds by constructing global analytic functions from the crystalline period map, proving compactness of their sublevel sets via a perfectoid normalization of Tate lattices, and showing that the resulting function map to affine space is finite. The key geometric inputs are the Fargues--Fontaine realization of the universal cover, a normalized determinant on the rank-two locus, and an integral PEL realization over W(F̅_p) used to produce bounded global Hodge generators. The integral constructions include the prime p=2.
ER -