论文标题
具有Weierstrass Torsion部分的可半椭圆表面的动机和算术概率
Motivic & Arithmetic probability of a semistable elliptic surface with a Weierstrass torsion section
论文作者
论文摘要
我们证明了新的尖锐渐近差异，用于计数可半固定的椭圆曲线，两个标记为$ \ infty $和$ 0 $的Weierstrass点，以及$ 0 $是2个扭转或3个扭矩的WeierStrass点，超过$ \ \ \ \ m athbb {f} _q（f} _q（t）$ airsed nifected nifectiand $ $ $ $ $ =我们考虑任何$ \ text {char}（k）\ neq 2,3 $在$ \ mathbb {p}^{1} $上挑选出非单词半固定的椭圆表面的动机概率{ In the end, we formulate an analogous heuristics on $\mathcal{Z}_{\mathbb{Q}}(\mathcal{B})$ for the ratio of the semistable elliptic curves with a marked rational 2-torsion or 3-torsion Weierstrass point at $0$ out of all semistable elliptic curves with a marked rational Weierstrass points at $ 0 $超过$ \ \ \ m athbb {q} $，通过全球字段类比的判别$δ$的有限高度。
We prove new sharp asymptotic for counting the semistable elliptic curves with two marked Weierstrass points at $\infty$ and $0$ and also the cases where $0$ is a 2-torsion or a 3-torsion marked Weierstrass point over $\mathbb{F}_q(t)$ by the bounded height of discriminant $Δ(X)$. We consider the motivic probabilities over any basefield $K$ with $\text{char}(K) \neq 2,3$ of picking a nonsingular semistable elliptic surface over $\mathbb{P}^{1}$ with two marked Weierstrass sections at $\infty$ and $0$ such that marked Weierstrass section at $0$ is 2-torsion or 3-torsion. In the end, we formulate an analogous heuristics on $\mathcal{Z}_{\mathbb{Q}}(\mathcal{B})$ for the ratio of the semistable elliptic curves with a marked rational 2-torsion or 3-torsion Weierstrass point at $0$ out of all semistable elliptic curves with a marked rational Weierstrass points at $0$ over $\mathbb{Q}$ by the bounded height of discriminant $Δ$ through the global fields analogy.
