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• W3141123372 abstract "In this paper we count the number $N_n^{text{tor}}(X)$ of $n$-dimensional algebraic tori over $mathbb{Q}$ whose Artin conductor of the associated character is bounded by $X$. This can be understood as a generalization of counting number fields of given degree by discriminant. We suggest a conjecture on the asymptotics of $N_n^{text{tor}}(X)$ and prove that this conjecture follows from Malle's conjecture for tori over $mathbb{Q}$. We also prove that $N_2^{text{tor}}(X) ll_{varepsilon} X^{1 + varepsilon}$, and this upper bound can be improved to $N_2^{text{tor}}(X) ll_{varepsilon} X (log X)^{1 + varepsilon}$ under the assumption of the Cohen-Lenstra heuristics for $p=3$." @default.
• W3141123372 created "2021-04-13" @default.
• W3141123372 creator A5004902602 @default.
• W3141123372 date "2021-04-07" @default.
• W3141123372 modified "2023-09-27" @default.
• W3141123372 title "Counting algebraic tori over $mathbb{Q}$ by Artin conductor" @default.
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