Non-isomorphic subfields of the BM and GGS maximal function fields
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915358308302848 |
|---|---|
| author | Beelen, Peter Drue, Tobias Montanucci, Maria Zini, Giovanni |
| author_facet | Beelen, Peter Drue, Tobias Montanucci, Maria Zini, Giovanni |
| contents | In 2016 Tafazolian et al. introduced new families of $\mathbb{F}_{q^{2n}}$-maximal function fields $\mathcal{Y}_{n,s}$ and $\mathcal{X}_{n,s,a,b}$ arising as subfields of the first generalized GK function field (GGS). In this way the authors found new examples of maximal function fields that are not isomorphic to subfields of the Hermitian function field. In this paper we construct analogous function fields $\tilde{\mathcal{Y}}_{n,s}$ and $\tilde{\mathcal{X}}_{n,s,a,b}$ as subfields of the second generalized GK function field (BM) and determine their automorphism groups. Using that the automorphism group is an invariant under isomorphism, we show that the function fields $\tilde{\mathcal{Y}}_{n,s}$ and ${\mathcal{Y}}_{n,s}$, as well as $\tilde{\mathcal{X}}_{n,s,a,b}$ and $\mathcal{X}_{n,s,a,b}$, are not isomorphic unless $m/s$ divides $q^2-q+1$ and $3$ divides $n$. In other words, the difference between the BM and GGS function fields can be found again at the level of the subfields that we consider. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-isomorphic subfields of the BM and GGS maximal function fields Beelen, Peter Drue, Tobias Montanucci, Maria Zini, Giovanni Algebraic Geometry 11G, 14G, 14H05 In 2016 Tafazolian et al. introduced new families of $\mathbb{F}_{q^{2n}}$-maximal function fields $\mathcal{Y}_{n,s}$ and $\mathcal{X}_{n,s,a,b}$ arising as subfields of the first generalized GK function field (GGS). In this way the authors found new examples of maximal function fields that are not isomorphic to subfields of the Hermitian function field. In this paper we construct analogous function fields $\tilde{\mathcal{Y}}_{n,s}$ and $\tilde{\mathcal{X}}_{n,s,a,b}$ as subfields of the second generalized GK function field (BM) and determine their automorphism groups. Using that the automorphism group is an invariant under isomorphism, we show that the function fields $\tilde{\mathcal{Y}}_{n,s}$ and ${\mathcal{Y}}_{n,s}$, as well as $\tilde{\mathcal{X}}_{n,s,a,b}$ and $\mathcal{X}_{n,s,a,b}$, are not isomorphic unless $m/s$ divides $q^2-q+1$ and $3$ divides $n$. In other words, the difference between the BM and GGS function fields can be found again at the level of the subfields that we consider. |
| title | Non-isomorphic subfields of the BM and GGS maximal function fields |
| topic | Algebraic Geometry 11G, 14G, 14H05 |
| url | https://arxiv.org/abs/2506.20210 |