论文标题
有限场上的空间曲线点的数量
A bound for the number of points of space curves over finite fields
论文作者
论文摘要
对于非分类不可约的曲线，$ d $ d $ in $ \ mathbb {p}^3 $ over $ \ mathbb {f} _q $，我们证明数字$ n_q（c）的$ n_q（c）$ of $ \ mathbb {f} f} _q $ - _q $ c $ $ c $ of $ c $满足$ n_q $ n_q（c）in_q+n_q+e+pality q+e q e+e q e+e q e+ce+e q。我们的结果改善了Homma在2012年获得的先前绑定的$ N_Q（C）\ LEQ（D-1）Q+1 $ $，并导致自然猜想概括了Sziklai的界限，以在有限场上的平面曲线点的数量。
For a non-degenerate irreducible curve $C$ of degree $d$ in $\mathbb{P}^3$ over $\mathbb{F}_q$, we prove that the number $N_q(C)$ of $\mathbb{F}_q$-rational points of $C$ satisfies the inequality $N_q(C) \leq (d-2)q+1$. Our result improves the previous bound $N_q(C) \leq (d-1)q+1$ obtained by Homma in 2012 and leads to a natural conjecture generalizing Sziklai's bound for the number of points of plane curves over finite fields.
