论文标题
高$ \ ell $ -torsion class groups toffunp
High $\ell$-torsion rank for class groups over function fields
论文作者
论文摘要
我们证明，在函数字段设置中，二次字段的类组中的$ \ ell $ torsion可以任意大。实际上，我们明确地产生了一个家庭 其$ \ ell $ rank的增长与属理论的环境相匹配，这可能是最好的。我们通过专门关注Artin-Schreir曲线$ y^2 = X^Q-X $来做到这一点。
We prove that in the function field setting, $\ell$-torsion in the class groups of quadratic fields can be arbitrarily large. In fact, we explicitly produce a family whose $\ell$-rank growth matches the growth in the setting of genus theory, which might be best possible. We do this by specifically focusing on the Artin-Schreir curves $y^2=x^q-x$.
