The \(a\)-number of \(y^n=x^m+x\) over finite fields

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...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Mosallaei, Behrooz, Farivar, Sepideh, Ghanbari, Farzaneh, Nourozi, Vahid
Format: Article
Language:English
Subjects:
Fields (mathematics)
Isomorphism
Operators (mathematics)
Online Access:Get full text
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Summary: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 \(\mathcal{X}\).
ISSN:2331-8422