|
| | | | |
| | | |
| Stat |
Members: 3665
Articles: 2'599'751
Articles rated: 2609
19 January 2025 |
|
| | | | |
|
Article overview
| |
|
|
Drinfeld Modular Curves Subordinate to Conjugacy Classes of Nilpotent Upper-Triangular Matrices | | Zhuo Chen
; Chuangqiang Hu
; Tao Zhang
; Xiaopeng Zheng
; | | Date: |
1 Sep 2023 | | Abstract: | We introduce normalized Drinfeld modular curves that parameterize rank $m$
Drinfeld modules compatible with a $T$-torsion structure arising from a given
conjugacy class of nilpotent upper-triangular $n imes n$ matrices with rank
$geqslant n-m$ over a finite field $mathbb{F}_q$. This creates a deep link
connecting the classification of nilpotent upper-triangular matrices and the
decomposition of Drinfeld modular curves. The conjugacy classes of nilpotent
upper-triangular matrices one-to-one corresponds to certain $T$-torsion flags,
and form a tree structure. As a result, the associated Drinfeld modular curves
are organized in the same tree. This generalizes the tower structure introduced
by Bassa, Beelen, Garcia, Stichtenoth, and others. Additionally,we prove the
geometric irreducibility of $(3,2)$-type normalized Drinfeld modular curves,
and characterize their associated function fields. | | Source: | arXiv, 2309.00432 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|
REGISTER