19
$\begingroup$

I am quite interested in moduli spaces for Rings and Ideals, a letter from Deligne to Bhargava is cited in Melanie Wood's thesis Moduli spaces for Rings and Ideals (pdf), studying the minimal free resolution of $n$ points in $\mathbb P^{n−2}$. It's also cited in the thesis of Kevin H. Wilson, Three perspectives on $n$ points in $\mathbb{P}^{n-2}$ (link) (after Theorem 135):

Such strong canonicity in these multiplicative structures has been implicitly used by many authors. For instance, Wright and Yukie [116] implicitly used this structure to parameterize rank $n$ rings over $\mathbb{Q}$. And Bhargava also implicitly relied on a much stronger canonicity (over $\mathbb{Z}$) in structuring his Higher Composition Laws [9, 10, 11, 14]. Perhaps the place where the idea of using such canonical multiplicative structures was first developed was in Deligne’s letter to Bhargava [41] which inspired Wood’s vast generalization in her thesis [114, 113, 112] extending Bhargava’s quadratic, cubic, and quartic Higher Composition Laws to arbitrary base schemes.

Where can I find a copy of this letter (or a short explanation of the idea)? Thank you very much.

$\endgroup$
6
  • 3
    $\begingroup$ for the record, a 2005 letter from Deligne to Bhargava is here $\endgroup$ Sep 24, 2020 at 20:47
  • 12
    $\begingroup$ You would think by now there'd be some centralized effort to gather all these different "personal communications" into a central database. $\endgroup$
    – R.P.
    Sep 24, 2020 at 20:48
  • 3
    $\begingroup$ They may or may not still have copies, but it would be worth writing to Deligne and Bhargava. $\endgroup$ Sep 24, 2020 at 22:46
  • 1
    $\begingroup$ can you give a link to the thesis you cite, if one exists. I also found the letter @CarloBeenakker found, presumably it is not the same one you want? $\endgroup$
    – kodlu
    Sep 25, 2020 at 0:01
  • 2
    $\begingroup$ Second @TheoJohnson-Freyd's suggestion. I am fairly certain Deligne is extremely organised and should still have the letter (but he may not be in the office much). $\endgroup$ Sep 25, 2020 at 4:23

1 Answer 1

27
$\begingroup$

The letter is here. Thanks to Will Sawin for alerting me to this request.

$\endgroup$
1
  • 3
    $\begingroup$ Welcome to MO! Thanks for posting this. $\endgroup$ Oct 6, 2020 at 14:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.