On Weierstrass semigroups of maximal Fermat function fields
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917299686998016 |
|---|---|
| author | Beelen, Peter Montanucci, Maria Braucke, Marie Frank vom |
| author_facet | Beelen, Peter Montanucci, Maria Braucke, Marie Frank vom |
| contents | In this article we explicitly determine the Weierstrass semigroup at any place of some $\mathbb{F}_{q^2}$-maximal Fermat function fields $\mathcal{F}_m$, namely for $m=(q+1)/2$ and $m=(q+1)/3$. These famous function fields arise as Galois subfields of the Hermitian function field, and even though they have been intensively studied in the literature, the Weierstrass semigroup at every place is still not fully known. Surprisingly enough this problem is in fact quite involved and $\mathcal{F}_m$ has many different types of Weierstrass semigroups. Moreover, its set of Weierstrass places is much richer than its set of rational places. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_24015 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Weierstrass semigroups of maximal Fermat function fields Beelen, Peter Montanucci, Maria Braucke, Marie Frank vom Algebraic Geometry Number Theory 11G20, 11R58, 14H05, 14H55 In this article we explicitly determine the Weierstrass semigroup at any place of some $\mathbb{F}_{q^2}$-maximal Fermat function fields $\mathcal{F}_m$, namely for $m=(q+1)/2$ and $m=(q+1)/3$. These famous function fields arise as Galois subfields of the Hermitian function field, and even though they have been intensively studied in the literature, the Weierstrass semigroup at every place is still not fully known. Surprisingly enough this problem is in fact quite involved and $\mathcal{F}_m$ has many different types of Weierstrass semigroups. Moreover, its set of Weierstrass places is much richer than its set of rational places. |
| title | On Weierstrass semigroups of maximal Fermat function fields |
| topic | Algebraic Geometry Number Theory 11G20, 11R58, 14H05, 14H55 |
| url | https://arxiv.org/abs/2602.24015 |