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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.

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    $\begingroup$ for the record, a 2005 letter from Deligne to Bhargava is here $\endgroup$ Commented Sep 24, 2020 at 20:47
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    $\begingroup$ 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.
    Commented Sep 24, 2020 at 20:48
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    $\begingroup$ They may or may not still have copies, but it would be worth writing to Deligne and Bhargava. $\endgroup$ Commented Sep 24, 2020 at 22:46
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    $\begingroup$ 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
    Commented Sep 25, 2020 at 0:01
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    $\begingroup$ 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). $\endgroup$ Commented Sep 25, 2020 at 4:23

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

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

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