Affiliation:
1. Department of Mathematics , University of British Columbia , Vancouver BC, V6T 1Z2 , Canada
Abstract
Abstract
This paper aims at studying the Iwasawa λ-invariant of the p-primary Selmer group.
We study the growth behavior of p-primary Selmer groups in p-power degree extensions over non-cyclotomic
ℤ
p
{\mathbb{Z}_{p}}
-extensions of a number field.
We prove a generalization of Kida’s formula in such a case.
Unlike the cyclotomic
ℤ
p
{\mathbb{Z}_{p}}
-extension, where all primes are finitely decomposed, in the
ℤ
p
{\mathbb{Z}_{p}}
-extensions we consider primes may be infinitely decomposed.
In the second part of this paper, we study the relationship of Iwasawa invariants with respect to congruences, obtaining refinements of the results of Greenberg, Vatsal and Kidwell.
As an application, we provide an algorithm for constructing elliptic curves with large anticyclotomic λ-invariant.
Our results are illustrated by explicit computation.
Subject
Applied Mathematics,General Mathematics
Reference44 articles.
1. C. Adelmann,
The Decomposition of Primes in Torsion Point Fields,
Lecture Notes in Math. 1761,
Springer, Berlin, 2004.
2. S. Ahmed, C. Aribam and S. Shekhar,
Root numbers and parity of local Iwasawa invariants,
J. Number Theory 177 (2017), 285–306.
3. M. Bertolini,
Selmer groups and Heegner points in anticyclotomic
𝐙
p
\mathbf{Z}_{p}
-extensions,
Compos. Math. 99 (1995), no. 2, 153–182.
4. M. Bertolini and H. Darmon,
Iwasawa’s main conjecture for elliptic curves over anticyclotomic
ℤ
p
\mathbb{Z}_{p}
-extensions,
Ann. of Math. (2) 162 (2005), no. 1, 1–64.
5. A. Bhave,
Analogue of Kida’s formula for certain strongly admissible extensions,
J. Number Theory 122 (2007), no. 1, 100–120.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献