Let be an odd prime number, and let be an elliptic curve defined over a number field such that has semistable reduction at every prime of above and is supersingular at least one prime above . Under appropriate hypotheses, we compute the Akashi series of the signed Selmer groups of over a -extension over a finite extension of . As a by-product, we also compute the Euler characteristics of these Selmer groups.
Soit un nombre premier impair, et soit une courbe elliptique définie sur un corps des nombres ayant réduction semi-stable en chaque premier de sur et ayant réduction supersingulière en au moins un premier sur . Sous des hypothèses appropriées, nous calculons la série d’Akashi des groupes de Selmer signés de sur une -extension d’une extension finie de . Comme un sous-produit, nous calculons aussi le caractéristique d’Euler de ces groupes de Selmer.
Revised:
Accepted:
Published online:
Mots-clés : Akashi series, signed Selmer groups, Euler characteristics.
Antonio Lei 1; Meng Fai Lim 2

@article{JTNB_2021__33_3.2_997_0, author = {Antonio Lei and Meng Fai Lim}, title = {Akashi series and {Euler} characteristics of signed {Selmer} groups of elliptic curves with semistable reduction at primes above $p$}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {997--1019}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {33}, number = {3.2}, year = {2021}, doi = {10.5802/jtnb.1185}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1185/} }
TY - JOUR AU - Antonio Lei AU - Meng Fai Lim TI - Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above $p$ JO - Journal de théorie des nombres de Bordeaux PY - 2021 SP - 997 EP - 1019 VL - 33 IS - 3.2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1185/ DO - 10.5802/jtnb.1185 LA - en ID - JTNB_2021__33_3.2_997_0 ER -
%0 Journal Article %A Antonio Lei %A Meng Fai Lim %T Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above $p$ %J Journal de théorie des nombres de Bordeaux %D 2021 %P 997-1019 %V 33 %N 3.2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1185/ %R 10.5802/jtnb.1185 %G en %F JTNB_2021__33_3.2_997_0
Antonio Lei; Meng Fai Lim. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1185/
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