The a-number of y^q2+q+1 = x^q2+1 + x^q over finite field

2024/01/23 by Nourozi, Vahid, Mosallaei, Behrooz
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.13707

Abstract

In this paper, we compute a formula for the a-number of curve \mathbbX given by the equation y^{q2 + q + 1} = x^{q2 + 1} - x^q over the finite field \mathbbF_q². The a-number is an invariant of the isomorphism class of the p-torsion group scheme. In this paper, we compute a closed formula for the a-number of \mathbbX using the action of the Cartier operator on H⁰(\mathbbX, Ω¹).

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