The $L$-polynomials of van der Geer--van der Vlugt curves in characteristic $2$
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_ | 1866914376903032832 |
|---|---|
| author | Ito, Tetsushi Takeuchi, Daichi Tsushima, Takahiro |
| author_facet | Ito, Tetsushi Takeuchi, Daichi Tsushima, Takahiro |
| contents | The van der Geer--van der Vlugt curves form a class of Artin--Schreier coverings of the projective line over finite fields. We provide an explicit formula for their $L$-polynomials in characteristic $2$, expressed in terms of characters of maximal abelian subgroups of associated Heisenberg groups. For this purpose, we develop new methods specific to characteristic $2$ that exploit the structure of the Heisenberg groups and the geometry of Lang torsors for $W_2$. As an application, we construct examples of curves in this family attaining the Hasse--Weil bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22036 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $L$-polynomials of van der Geer--van der Vlugt curves in characteristic $2$ Ito, Tetsushi Takeuchi, Daichi Tsushima, Takahiro Number Theory Algebraic Geometry The van der Geer--van der Vlugt curves form a class of Artin--Schreier coverings of the projective line over finite fields. We provide an explicit formula for their $L$-polynomials in characteristic $2$, expressed in terms of characters of maximal abelian subgroups of associated Heisenberg groups. For this purpose, we develop new methods specific to characteristic $2$ that exploit the structure of the Heisenberg groups and the geometry of Lang torsors for $W_2$. As an application, we construct examples of curves in this family attaining the Hasse--Weil bound. |
| title | The $L$-polynomials of van der Geer--van der Vlugt curves in characteristic $2$ |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2505.22036 |