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- W4313484603 abstract "Cohen, Lenstra, and Martinet have given conjectures for the distribution of class groups of extensions of number fields, but Achter and Malle have given theoretical and numerical evidence that these conjectures are wrong regarding the Sylow $p$-subgroups of the class group when the base number field contains $p$th roots of unity. We give complete conjectures of the distribution of Sylow $p$-subgroups of class groups of extensions of a number field when $p$ does not divide the degree of the Galois closure of the extension. These conjectures are based on $qrightarrowinfty$ theorems on these distributions in the function field analog and use recent work of the authors on explicitly giving a distribution of modules from its moments. Our conjecture matches many, but not all, of the previous conjectures that were made in special cases taking into account roots of unity." @default.
- W4313484603 created "2023-01-06" @default.
- W4313484603 creator A5053317769 @default.
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- W4313484603 date "2023-01-02" @default.
- W4313484603 modified "2023-10-01" @default.
- W4313484603 title "Conjectures for distributions of class groups of extensions of number fields containing roots of unity" @default.
- W4313484603 doi "https://doi.org/10.48550/arxiv.2301.00791" @default.
- W4313484603 hasPublicationYear "2023" @default.
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