ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group
J. Klüners, J. Wang, Proceedings of the American Mathematical Society 150 (2022) 2793–2805.
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Klüners, JürgenLibreCat;
Wang, Jiuya
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Abstract
We describe the relations among the ℓ-torsion conjecture, a conjecture of Malle giving an upper bound for the number of extensions, and the discriminant multiplicity conjecture. We prove that the latter two conjectures are equivalent in some sense. Altogether, the three conjectures are equivalent for the class of solvable groups. We then prove the ℓ-torsion conjecture for ℓ-groups and the other two conjectures for nilpotent groups.
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Journal Title
Proceedings of the American Mathematical Society
Volume
150
Issue
7
Page
2793-2805
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Klüners J, Wang J. ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group. Proceedings of the American Mathematical Society. 2022;150(7):2793-2805. doi:10.1090/proc/15882
Klüners, J., & Wang, J. (2022). ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group. Proceedings of the American Mathematical Society, 150(7), 2793–2805. https://doi.org/10.1090/proc/15882
@article{Klüners_Wang_2022, title={ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group}, volume={150}, DOI={10.1090/proc/15882}, number={7}, journal={Proceedings of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Wang, Jiuya}, year={2022}, pages={2793–2805} }
Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number Fields with an ℓ-Group as Galois Group.” Proceedings of the American Mathematical Society 150, no. 7 (2022): 2793–2805. https://doi.org/10.1090/proc/15882.
J. Klüners and J. Wang, “ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group,” Proceedings of the American Mathematical Society, vol. 150, no. 7, pp. 2793–2805, 2022, doi: 10.1090/proc/15882.
Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number Fields with an ℓ-Group as Galois Group.” Proceedings of the American Mathematical Society, vol. 150, no. 7, American Mathematical Society (AMS), 2022, pp. 2793–805, doi:10.1090/proc/15882.
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