Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above p

Abstract

Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above p Tome 33, n o 3.2 (2021), p. 997-1019. <http://jtnb.centre-mersenne.org/item?id=JTNB_2021__33_3.2_997_0> © Société Arithmétique de Bordeaux, 2021, tous droits réservés.L'accès aux articles de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.centre-mersenne.org/), implique l'accord avec les conditions générales d'utilisation (http://jtnb. centre-mersenne.org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l'utilisation à fin strictement personnelle du copiste est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. cedramArticle mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques http://www.centre-mersenne.org/

Higher codimension Iwasawa theory for elliptic curves with supersingular reduction

“…We will accomplish the task by taking the limit suitably. See Remark 4.9 for a relation with other previous work (Lei and Lim [15] and Lim [17]). Finally in §4.4, we briefly observe ordinary analogues.…”

“…As in §1.1, we write X ǫ and X ǫ S for the Pontryagin duals of Sel ǫ (E/K ∞ ) and Sel ǫ S (E/K ∞ ), respectively. As stated in [15,Conjecture 4.11], it is natural to conjecture the following.…”

“…As already remarked, the key idea to define the signed Selmer groups is given by Kobayashi [14], and there are a number of subsequent studies to generalize the idea. The definition below basically follows [15,Definition 4.7].…”

“…The original work of Kobayashi dealt with the case where F = Q, and B. D. Kim [12] gave an extension to the case where F is an imaginary quadratic field. The definition for general F was given by Lei and Lim [15].…”

On the cohomology of Kobayashi’s plus/minus norm groups and applications

“…These plus/minus norm groups are integral components in the definition of the signed Selmer groups. In particular, they come up in the local conditions at the supersingular primes in the definition of the Selmer groups, which were originally defined by Kobayashi [21], and later studied by other authors (for instances, see [2,[17][18][19][20][22][23][24][25]). In this paper, we will study the cohomology of the plus/minus norm groups, and our results are as follow.…”