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In Keisuke Arai's 2007 paper "On uniform lower bound of the Galois images associated to elliptic curves", which can be found on ArXiv, Arai makes the following citation:

K. Nakata. On the 2-adic representation associated to an elliptic curve defined over $\mathbb{Q}$. (Japanese), Number Theory Symposium in Kinosaki, December 1979, 221-235.

Arai says that the Galois action on the 2-adic Tate module of a non-CM curve over $\mathbb{Q}$ whose 2-torsion points are all defined over $\mathbb{Q}$ is studied in the above article.

The problem is that this article seems completely inaccessible to me, even after asking the help of several librarians. In addition, I can't read Japanese, so it's possible that getting hold of the article would be useless for me anyway.

So I'm wondering, can anyone here either somehow point me to a copy of the article (in English), or at least state the main results concerning 2-adic representations associated to elliptic curves over $\mathbb{Q}$ which can be found in the article? Thanks very much!

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  • $\begingroup$ This paper seems likely to be hard to find. It's not in MathSciNet, and math genealogy only lists one math Ph.D. with the name K. Nakata. This is a certain Keiko Nakata who earned a Ph.D. in 2007 and works in theoretical computer science. $\endgroup$
    – Jeremy Rouse
    Commented May 30, 2014 at 20:00
  • $\begingroup$ Part of the reason for my concern is that I happen to have written a paper about $2$-adic Galois representations for elliptic curves over $\mathbb{Q}$. (There's a preprint here.) $\endgroup$
    – Jeremy Rouse
    Commented May 30, 2014 at 20:03
  • $\begingroup$ Jeremy, so just to be clear, you don't know anything about what Nakata proved in this paper? $\endgroup$
    – Jeff Yelton
    Commented Jun 3, 2014 at 3:12
  • $\begingroup$ I'm pretty sure the K. Nakata we're looking for can't be Keiko Nakata... $\endgroup$
    – Jeff Yelton
    Commented Jun 3, 2014 at 3:16
  • $\begingroup$ @Jeff-I do not know anything about what Nakata proved in this paper. $\endgroup$
    – Jeremy Rouse
    Commented Jun 3, 2014 at 21:23

2 Answers 2

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Kumiko Nishioka is right name. Please take a look the folloing paper http://projecteuclid.org/euclid.jmsj/1230396544.

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This revision (June 2015) is mostly to say that I've verified the answer by ell. I found the Proceedings volume in question in the U. Tokyo library. It is basically a bound volume of photocopies of handwritten notes in Japanese. I made a "scan" with my phone, so if you want a copy of the Japanese version, just ask. The main theorems are identical, but the arguments in the English version are substantially more detailed, and the list of references was expanded.

Old Partial answer: You can find a copy at one of the libraries listed here. If I don't forget, I can take a look late next month when I go to U. Tokyo for a conference. You can also buy a copy of the proceedings for 4500 Yen (plus shipping).

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