Compactification of the Bruhat-Tits building of PGL by seminorms

Annette Werner

备注：: 18 pages

英文摘要：

We construct a compactification of the Bruhat-Tits building associated to the group PGL(V) which can be identified with the space of homothety classes of seminorms on V endowed with the topology of pointwise convergence. Then we define a continuous map from the projective space to this compactification which extends the reduction map from Drinfeld's p-adic symmetric domain to the building.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Compactification of the Bruhat-Tits building of PGL by lattices of smaller rank

We construct a compactification of the Bruhat-Tits building associated to the group PGL(V) by attaching all the Bruhat-Tits buildings of PGL(W) for non-trivial subspaces W of V as a boundary.

2001-04-03math.AGmath.NT

Non-Archimedean intersection indices on projective spaces and the Bruhat-Tits building for PGL

Inspired by Manin's approach towards a geometric interpretation of Arakelov theory at infinity, we interpret in this paper non-Archimedean local intersection numbers of linear cycles in $P^{n-1}$ with the combinatorial geometry of the Bruhat-Tits building associated to PGL(n).

2002-04-11math.AGmath.NT

Invitation to higher local fields, Part II, section 3: The Bruhat-Tits buildings over higher dimensional local fields

This work introduces author's theory of Bruhat-Tits buildings over higher dimensional local fields. The theory is illustrated with the buildings for PGL(2) and PGL(3) for one- and two-dimensional local fields.

2000-12-18math.AGmath.NT

Mustafin Varieties

A Mustafin variety is a degeneration of projective space induced by a point configuration in a Bruhat-Tits building. The special fiber is reduced and Cohen-Macaulay, and its irreducible components form interesting combinatorial patterns. For configurations that lie in one apartment, these patterns are regular mixed subdivisions of scaled simplices, and the Mustafin variety is a twisted Veronese variety built from such a subdivision. This connects our study to tropical and toric geometry. For general configurations, the irreducible components of the special fiber are rational varieties, and any…

2011-04-11math.AG

Compactifications of S-arithmetic quotients for the projective general linear group

Let F be a global field, and let S be a finite set of places of F containing all archimedean places. Consider the product X of the symmetric spaces and Bruhat-Tits buildings for PGL_d of the completions of F at archimedean and non-archimedean places in S, respectively. We construct compactifications of the quotient of X by S-arithmetic subgroups of PGL_d(F). The constructions make delicate use of reductive Borel-Serre spaces for archimedean places and polyhedral and seminorm compactifications at nonarchimedean places. We also briefly discuss a few potential applications of our compacifications…

2016-12-09math.AGmath.GRmath.NT

Vector Bundles and Arithmetical Groups I. The higher Bruhat-Tits tree

We define and study a simplicial complex which is a homogeneous space for the group $PGL(2, K)$ over a two-dimensional local field $K$. The complex is a generalization of the tree studied by F. Bruhat, J. Tits, J.-P. Serre and P. Cartier in the 60's and early 70's. Such complex can be canonically attached to the triples $x \in C \subset X$ where $X$ is an algebraic surface, $C$ is an irreducible curve and $x$ is a smooth point on $C$ and $X$. This construction can be used for a description of the isomorphism set of vector bundles on $X$.

1996-05-07alg-geommath.AGmath.QA

更多相关论文收起更多论文

超曲面模型与布鲁哈-蒂茨建筑模型

Models of hypersurfaces and Bruhat-Tits buildings

Institute for Algebra and Number Theory, Ulm University（乌尔姆大学代数与数论研究所）

本文提出了一种基于布鲁哈-蒂茨建筑的半稳定超曲面模型构造方法，并应用于p进数域上的平面曲线研究。

2026-02-09math.AG

Buildings、赋值拟阵与热带线性空间

Buildings, valuated matroids, and tropical linear spaces

本文研究了 Affine Bruhat--Tits buildings 与赋值拟阵的联系，证明了半范数空间是所有热带化线性嵌入的极限，并验证了其作为通用可实现赋值拟阵的热带线性空间本质。

2023-04-18math.AGmath.CO