The $a$-number of $y^n=x^m+x$ over finite fields

Behrooz Mosallaei; Sepideh Farivar; Farzaneh Ghanbari; Vahid Nourozi

The $a$-number of $y^n=x^m+x$ over finite fields

Number Theory 2024-06-28 v2 Algebraic Geometry

Authors: Behrooz Mosallaei , Sepideh Farivar , Farzaneh Ghanbari , Vahid Nourozi

Abstract

This paper presents a formula for $a$ -number of certain maximal curves characterized by the equation $y^{\frac{q+1}{2}} = x^m + x$ over the finite field $\mathbb{F}_{q^2}$ . $a$ -number serves as an invariant for the isomorphism class of the $p$ -torsion group scheme. Utilizing the action of the Cartier operator on $H^0(\mathcal{X}, \Omega^1)$ , we establish a closed formula for $a$ -number of $\mathcal{X}$ .

Keywords

a-number maximal curves finite fields Cartier operator p-torsion group scheme

Cite

@article{arxiv.2404.08149,
  title  = {The $a$-number of $y^n=x^m+x$ over finite fields},
  author = {Behrooz Mosallaei and Sepideh Farivar and Farzaneh Ghanbari and Vahid Nourozi},
  journal= {arXiv preprint arXiv:2404.08149},
  year   = {2024}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2401.01305

The $a$-number of $y^n=x^m+x$ over finite fields

Abstract

Keywords

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