The $a$-number of $y^n=x^m+x$ over finite fields
| Autor: | Mosallaei, Behrooz, Farivar, Sepideh, Ghanbari, Farzaneh, Nourozi, Vahid |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\mathcal{X}$. Comment: arXiv admin note: substantial text overlap with arXiv:2401.01305 |
| Databáze: | arXiv |
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