# Reference request: Deligne's reconstruction theorem

I've heard this result referenced a few times on MO now. It is supposed to be a theorem of Deligne that gives some natural conditions under which an (abelian?) tensor category $C$ is the category of representations of a Lie superalgebra, or perhaps an affine supergroup scheme. However, Deligne's original paper is in French, which I can't read, and I have not been able to find in English even a statement of this theorem. Can anyone help me out?

(Motivation: I want to verify the conditions for categories of bounded chain complexes.)

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Why not do this: ehow.com/how_7470614_translate-french-pdfs-english.html –  Damien Aug 11 '11 at 4:58
I was wondering if you couldn’t give the complete reference of the original article. (And if possible a link.) –  Pierre-Yves Gaillard Aug 11 '11 at 5:27
@Qiaochu: Why not cite the French paper if you know it? Someone here might be kind enough to translate the relevant bit. –  Zhen Lin Aug 11 '11 at 5:27
Well, I don't know how to interpret the whole super-thing and how to produce an appropriate fiber functor on the category of bounded chain complexes, but the notes by Breen on Tannakian categories look pretty decent. –  t.b. Aug 11 '11 at 9:28
Here is the original article: ams.org/distribution/mmj/vol2-2-2002/deligne.pdf –  plusepsilon.de Aug 11 '11 at 11:08