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The Rank of the Cartier operator on Picard Curves

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arxiv 2306.07823 v2 pith:PCIAKXCX submitted 2023-06-13 math.AG math.NT

Vahid Nourozi , Farhad Rahmati This is my paper · ORCID
classification math.AGmath.NT
keywords mathcalcartiercurvesnumberoperatorpicardactionalgebraic
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abstract

For an algebraic curve $\mathcal{X}$ defined over an algebraically closed field of characteristic $p > 0$, the $a$-number $a(\mathcal{X})$ is the dimension of the space of exact holomorphic differentials on $\mathcal{X}$. We compute the $a$-number for a family of certain Picard curves, using the action of the Cartier operator on $H^0(\mathcal{X},\Omega^1)$.

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  1. Reinforcement Learning Enhanced Greedy Decoding for Quantum Stabilizer Codes over $\mathbb{F}_q$

    quant-ph 2025-06 reject novelty 3.0 of 10

    A claimed [[27,13,4]]_3 qutrit code from separated-polynomial curves and an RL-on-Greedy decoder are presented, but internal math inconsistencies and missing simulation data undermine the claims.

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