通过阿廷导体计数Q上代数环面的一个上界
An upper bound for counting algebraic tori over $\mathbb{Q}$ by Artin conductor
AI总结：
该研究给出Q上n维代数环面同构类数的上界，其证明借助ChatGPT 5.6 Pro的迭代对话完成。
AI中文摘要：
设N_n^tor(X)为Q上n维代数环面的同构类数，其阿廷导体不超过X。我们证明存在绝对常数C>0，对每个≥2的正整数n，N_n^tor(X)≪_n X^{exp(C(log n)^2)}。主要结果的证明通过与ChatGPT 5.6 Pro的迭代对话完成。
英文摘要：
Let $N_n^{\mathrm{tor}}(X)$ be the number of isomorphism classes of $n$-dimensional algebraic tori over $\mathbb{Q}$ whose Artin conductor is bounded by $X$. We prove that there is an absolute constant $C>0$ such that, for every positive integer $n \ge 2$, $N_n^{\mathrm{tor}}(X)\ll_n X^{\exp(C(\log n)^2)}$. The proofs of the main results were developed through an iterative dialogue with ChatGPT 5.6 Pro.
