A while back I mentioned the usefulness of version control software in my work (see also the current discussion at the Secret Blogging Seminar). Now here is a True Life example of what it can do: Vijay Patankar wrote to me today, pointing out that in my paper Weil numbers generated by other Weil numbers and torsion fields of abelian varieties, I claim (misquoting slightly for typographical reasons):

Remark 3.9. In

[K1], the question of the “splitting behaviour” of a simple abelian varietyA/at all primes is also raised: is it true that the reduction moduloQpofAremains simple for almost allp? In fact, the “horizontal” statements of Chavdarov can already deal with this. For instance, this property holds ifA/has the property that the Galois group of the fieldQgenerated by the points ofQ(A[n])n-torsion ofAis equal to Sp(2g,) for any sufficiently large primeZ/nZn.

Here, the citation **[K1]** refers to my earlier paper Some Local-Global Applications of Kummer Theory, but as he pointed out, the question is not mentioned anywhere there… So where did it go?

I have no memory at all of what happened, but thanks to SVN’s history facility, I have been able to reconstitute the outline of this nanoscopic academic drama: first, in late 2001, I added a remark about this problem in the final section, among other questions suggested by the paper:

r416 | emmanuel | 2001-09-13 08:52:44 +0200 (Thu, 13 Sep 2001) | 3 lines

416 emmanuel \item Given an abelian variety $A/k$ over un number field, how does

416 emmanuel its decomposition in simple factors relate to that of its reductions

416 emmanuel in general? In particular, assuming $A$ to be $k$-simple, is the set

416 emmanuel of primes $\ideal{p}$ with $A_{\ideal{p}}$ reducible finite, or of

416 emmanuel density $0$?

Here, the first line is an excerpt from the log file which records the history of every file under version control (it is produced by the `svn log`

command); the number 416 is the “revision number” which identifies at what point in time the changes corresponding to this “commit” were made.

The next lines (which, in fact, come chronologically first in the unraveling of the mystery, as they tell which revision number to look at to find the exact date) are obtained by the `svn blame`

command: for each line of a file, this indicates (1) at which revision the line was added (or last changed); (2) who did the change.

Then, in late 2002, just before sending the corrected version to the publisher, I commented out this question:

r1831 | emmanuel | 2002-11-14 21:16:41 +0100 (Thu, 14 Nov 2002) | 2 lines

1831 emmanuel %\item Given an abelian variety $A/k$ over un number field, how does

1831 emmanuel % its decomposition in simple factors relate to that of its reductions

1831 emmanuel % in general? In particular, assuming $A$ to be $k$-simple, is the set

1831 emmanuel % of primes $\ideal{p}$ with $A_{\ideal{p}}$ reducible finite, or of

1831 emmanuel % density $0$?

I still don’t know why I ended up doing this; indeed, two years later, I was convinced I had not done so, when I wrote the excerpt above from my other paper (the date can again be determined using SVN). In passing, this confirms the principle (which I try to adhere to usually) that one should always give a complete detailed reference to any outside work – even if it’s your own. If I had taken the trouble of trying to locate the page or section number for this question, I would have realized it was missing…

Finally, if the question seems of interest, this paper of Murty and Patankar develops it further.

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