Extending Azumaya algebras associated to arithmetic 2-bridge links
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908650229989376 |
|---|---|
| author | Wan, Jiayu |
| author_facet | Wan, Jiayu |
| contents | Let Γ be a finitely generated group and consider the set of all characters of representations
of Γ into SL2(C). This set, denoted by X(Γ), admits an algebraic structure and is called the character
variety of Γ. When Γ is the fundamental group of a hyperbolic 3-manifold M, X(Γ) turns out to
be a powerful tool in the study of the geometry and topology of M. Chinburg-Reid-Stover have
borrowed tools from algebraic and arithmetic geometry to understand algebraic and number-theoretic
properties of the canonical curves of X(Γ). In this paper, we will partly generalize their results to
certain hyperbolic link complements, and prove that the associated canonical quaternion algebra will
not extend to an Azumaya algebra over the canonical surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending Azumaya algebras associated to arithmetic 2-bridge links Wan, Jiayu Geometric Topology Let Γ be a finitely generated group and consider the set of all characters of representations of Γ into SL2(C). This set, denoted by X(Γ), admits an algebraic structure and is called the character variety of Γ. When Γ is the fundamental group of a hyperbolic 3-manifold M, X(Γ) turns out to be a powerful tool in the study of the geometry and topology of M. Chinburg-Reid-Stover have borrowed tools from algebraic and arithmetic geometry to understand algebraic and number-theoretic properties of the canonical curves of X(Γ). In this paper, we will partly generalize their results to certain hyperbolic link complements, and prove that the associated canonical quaternion algebra will not extend to an Azumaya algebra over the canonical surfaces. |
| title | Extending Azumaya algebras associated to arithmetic 2-bridge links |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2511.09937 |