Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above p
Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 3.2, pp. 997-1019.

Let p be an odd prime number, and let E be an elliptic curve defined over a number field F such that E has semistable reduction at every prime of F above p and is supersingular at least one prime above p. Under appropriate hypotheses, we compute the Akashi series of the signed Selmer groups of E over a p d -extension over a finite extension F of F . As a by-product, we also compute the Euler characteristics of these Selmer groups.

Soit p un nombre premier impair, et soit E une courbe elliptique définie sur un corps des nombres F ayant réduction semi-stable en chaque premier de F sur p et ayant réduction supersingulière en au moins un premier sur p. Sous des hypothèses appropriées, nous calculons la série d’Akashi des groupes de Selmer signés de E sur une p d -extension d’une extension finie F de F . Comme un sous-produit, nous calculons aussi le caractéristique d’Euler de ces groupes de Selmer.

Received:
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Accepted:
Published online:
DOI: 10.5802/jtnb.1185
Classification: 11G05, 11R23
Keywords: Akashi series, signed Selmer groups, Euler characteristics.
Lei, Antonio 1; Lim, Meng Fai 2

1 Département de Mathématiques et de Statistique Université Laval Pavillion Alexandre-Vachon 1045 Avenue de la Médecine Québec, QC Canada G1V 0A6
2 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences Central China Normal University Wuhan, 430079 P.R.China
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Lei, Antonio; Lim, Meng Fai. Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above $p$. Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 3.2, pp. 997-1019. doi : 10.5802/jtnb.1185. http://www.numdam.org/articles/10.5802/jtnb.1185/

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