5
$\begingroup$

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.)

  • 0
    Why not do this: http://www.ehow.com/how_7470614_translate-french-pdfs-english.html2011-08-11
  • 0
    How about this: http://books.google.com/books?id=3TGxxHmX68oC&pg=PA517&lpg=PA517&dq=deligne's+reconstruction+theorem+tensor+category&source=bl&ots=gu5Phkupzu&sig=9X9iFNaAzOKq4Bhrgt7hKmOxNG0&hl=en&ei=s2JDTpb0DKP10gGcnI3NCQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDMQ6AEwAw#v=onepage&q&f=false2011-08-11
  • 0
    @Damien: I saw that, but I don't think it's the result I'm thinking of. The word "super" is fairly important.2011-08-11
  • 3
    I was wondering if you couldn’t give the complete reference of the original article. (And if possible a link.)2011-08-11
  • 2
    @Qiaochu: Why not cite the French paper if you know it? Someone here might be kind enough to translate the relevant bit.2011-08-11
  • 0
    @Pierre-Yves: People always cite Deligne's monumental *[Catégories tannakiennes](http://dx.doi.org/10.1007/978-0-8176-4575-5_3)*. I don't have the expertise to even recognize the theorem in there.2011-08-11
  • 0
    @Theo: Thanks. I wonder if the OP shouldn’t rephrase his question.2011-08-11
  • 1
    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](http://books.google.com/books?id=v2CuklFFV5IC&pg=pa337)* look pretty decent.2011-08-11
  • 2
    Here is the original article: http://www.ams.org/distribution/mmj/vol2-2-2002/deligne.pdf2011-08-11

1 Answers 1

5

http://arxiv.org/abs/math/0401347