On fine Selmer groups and the greatest common divisor of signed and chromatic $p$-adic $L$-functions
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- by Antonio Lei and R. Sujatha PDF
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Abstract:
Let $E/\mathbb {Q}$ be an elliptic curve and $p$ an odd prime where $E$ has good supersingular reduction. Let $F_1$ denote the characteristic power series of the Pontryagin dual of the fine Selmer group of $E$ over the cyclotomic $\mathbb {Z}_p$-extension of $\mathbb {Q}$ and let $F_2$ denote the greatest common divisor of Pollack’s plus and minus $p$-adic $L$-functions or Sprung’s sharp and flat $p$-adic $L$-functions attached to $E$, depending on whether $a_p(E)=0$ or $a_p(E)\ne 0$. We study a link between the divisors of $F_1$ and $F_2$ in the Iwasawa algebra. This gives new insights into problems posed by Greenberg and Pollack–Kurihara on these elements.References
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Additional Information
- Antonio Lei
- Affiliation: Département de Mathématiques et de Statistiques, Université Laval, Pavillon Alexandre-Vachon, 1045 Avenue de la Médecine, Québec, Quebec City G1V 0A6, Canada
- MR Author ID: 902727
- ORCID: 0000-0001-9453-3112
- Email: antonio.lei@mat.ulaval.ca
- R. Sujatha
- Affiliation: Department of Mathematics, 1984 Mathematics Road, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
- MR Author ID: 293023
- ORCID: 0000-0003-1221-0710
- Email: sujatha@math.ubc.ca
- Received by editor(s): May 12, 2020
- Received by editor(s) in revised form: December 14, 2020
- Published electronically: May 13, 2021
- Additional Notes: Both authors also gratefully acknowledged support of their respective NSERC Discovery Grants.
- Communicated by: Romyar Sharifi
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 3235-3243
- MSC (2020): Primary 11R23, 11G05
- DOI: https://doi.org/10.1090/proc/15480
- MathSciNet review: 4273131