论文标题
德林菲尔德模块的扭转点的加洛伊斯标准
Galois criterion for torsion points of Drinfeld modules
论文作者
论文摘要
在本文中，我们制定了Lang提出的一个问题的Drinfeld模块类似物，并由Katz研究了Abelian品种在数字领域上存在理性点。给定最大的理想$ \ fl $ $ \ f_q [t] $，这个问题本质上询问，要提高$ \ f_q（t）$超过$ \ f_q（t）$的drinfeld模块$ ϕ $是否包含一个有理$ \ fl $ - torsion点，如果将$ copt $ \ f_q $ \ f_q [t y $ \ f_q [t]与Abelian品种类似，我们表明，如果德林菲尔德模块的排名为$ 2 $，则答案是积极的，但如果排名为$ 3 $，则答案为负。此外，对于排名$ 3 $ DRINFELD模块，我们将答案为正的情况分类。
In this paper, we formulate the Drinfeld module analogue of a question raised by Lang and studied by Katz on the existence of rational points on abelian varieties over number fields. Given a maximal ideal $\fl$ of $\F_q[T]$, the question essentially asks whether, up to isogeny, a Drinfeld module $ϕ$ over $\F_q(T)$ contains a rational $\fl$-torsion point if the reduction of $ϕ$ at almost all primes of $\F_q[T]$ contains a rational $\fl$-torsion point. Similar to the case of abelian varieties, we show that the answer is positive if the rank of the Drinfeld module is $2$, but negative if the rank is $3$. Moreover, for rank $3$ Drinfeld modules we classify those cases where the answer is positive.
