activity
20012020
most citedThe GL_2 main conjecture for elliptic curves without complex multiplication

188 citations · 232 across the 7 of their papers we have counts for

collaborators

8 papers

math.NT2020

Classical Iwasawa theory and infinite descent on a family of abelian varieties

John Coates, Jianing Li, Yongxiong Li

For primes , the present manuscript shows that elementary methods enable one to prove surprisingly strong results about the Iwasawa theory of the Gross family o…

math.NT2019★ 1 cited

Non-vanishing theorems for central -values of some elliptic curves with complex multiplication II

John Coates, Yongxiong Li

Let be any prime , , and let be the Hilbert class field of . Let be the Gross elliptic curve defined over with com…

math.NT2018★ 7 cited

Non-vanishing theorems for central -values of some elliptic curves with complex multiplication

John Coates, Yongxiong Li

The paper uses Iwasawa theory at the prime to prove non-vanishing theorems for the value at of the complex -series of certain quadratic twists of the Gross family of…

math.NT2013

Quadratic Twists of Elliptic Curves

John Coates, Yongxiong Li, Ye Tian +1

In this paper, we show that Tian's induction method can be generalised to study the Birch-Swinnerton-Dyer conjecture for the quadratic twists, both with global root number and…

math.NT2013★ 6 cited

On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication

John Coates, Minhyong Kim, Zhibin Liang +1

Given an elliptic curve E over Q with complex multiplication having good reduction at 2, we investigate the 2-adic valuation of the algebraic part of the L-value at 1 for a family…

math.NT2008★ 28 cited

Selmer varieties for curves with CM Jacobians

John Coates, Minhyong Kim

We study the Selmer variety associated to a canonical quotient of the $\Q_p$-pro-unipotent fundamental group of a smooth projective curve of genus at least two defined over $\Q$ wh…