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ON THE SELMER GROUP OF A CERTAIN $p$-ADIC LIE EXTENSION

Published online by Cambridge University Press:  27 February 2019

AMALA BHAVE*
Affiliation:
School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India-110067 email amalasarma@gmail.com
LACHIT BORA
Affiliation:
School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India-110067 email boralachit3@gmail.com

Abstract

Let $E$ be an elliptic curve over $\mathbb{Q}$ without complex multiplication. Let $p\geq 5$ be a prime in $\mathbb{Q}$ and suppose that $E$ has good ordinary reduction at $p$. We study the dual Selmer group of $E$ over the compositum of the $\text{GL}_{2}$ extension and the anticyclotomic $\mathbb{Z}_{p}$-extension of an imaginary quadratic extension as an Iwasawa module.

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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Footnotes

The first author acknowledges the support of DST PURSE and UPE II grants; the second author is supported by a UGC-BSR fellowship.

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