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arXiv 2001.093042020-01math.NT

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

Antonio Lei, Meng Fai Lim

备注：: Some minor corrections and revisions; 19 pages
发表信息：: Journal de Théorie des Nombres de Bordeaux (Proceedings of Iwasawa 2019), Tome 33 (2021) no. 3.2, pp. 997-1019
DOI：: 10.5802/jtnb.1185

英文摘要：

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 at least one prime above $p$. Under appropriate hypotheses, we compute the Akashi series of the signed Selmer groups of $E$ over a $\mathbb{Z}_p^d$-extension over a finite extension $F$ of $F'$. As a by-product, we also compute the Euler characteristics of these Selmer groups.

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