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Relative p-class groups and p-Selmer groups

Let E be an elliptic curve with j-invariant 1728 or 0 and let E˜ be a kth twist of E. We show that for any prime p of good reduction of E˜, a degree k relative p-class group and the root number of E˜ determines the dimension of the p-Selmer group of E˜. Consequently, we relate congruent number (resp...

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Bibliographic Details
Main Authors: De, Debajyoti (Author) , Majumdar, Dipramit (Author) , Mondal, Sudipa (Author)
Format: Article (Journal)
Language:English
Published: April 2026
In: Journal of pure and applied algebra
Year: 2026, Volume: 230, Issue: 4, Pages: 1-32
ISSN:1873-1376
DOI:10.1016/j.jpaa.2026.108222
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jpaa.2026.108222
Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0022404926000538
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Author Notes:Debajyoti De, Dipramit Majumdar, Sudipa Mondal
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Summary:Let E be an elliptic curve with j-invariant 1728 or 0 and let E˜ be a kth twist of E. We show that for any prime p of good reduction of E˜, a degree k relative p-class group and the root number of E˜ determines the dimension of the p-Selmer group of E˜. Consequently, we relate congruent number (resp. cube sum) problem with relative p-class group of quadratic (resp. cubic) extensions. In another application, we construct families of large rank p-class group. We also construct infinitely many number fields of degree d which satisfies Golod-Shafarevich bound for p=3,5 such that (d,p)=1.
Item Description:Online verfügbar: 16. März 2026, Artikelversion: 19. März 2026
Gesehen am 29.04.2026
Physical Description:Online Resource
ISSN:1873-1376
DOI:10.1016/j.jpaa.2026.108222

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