On unit signatures and narrow class groups of odd degree abelian number fields

Breen, Benjamin; Varma, Ila; Voight, John

doi:10.1090/btran/90

On unit signatures and narrow class groups of odd degree abelian number fields
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by Benjamin Breen, Ila Varma and John Voight; with an appendix by Noam Elkies

Trans. Amer. Math. Soc. Ser. B 10 (2023), 86-128

DOI: https://doi.org/10.1090/btran/90

Published electronically: February 3, 2023

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Abstract:

For an abelian number field of odd degree, we study the structure of its $2$-Selmer group as a bilinear space and as a Galois module. We prove structural results and make predictions for the distribution of unit signature ranks and narrow class groups in families where the degree and Galois group are fixed.

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Transactions of the American Mathematical Society Series B

On unit signatures and narrow class groups of odd degree abelian number fields
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Abstract: