1982 Original authentic typed version.
2012 TeXed, corrected, original numbering retained.
2018 TeXed, corrected, updated, original numbering retained.
2022 corrected, updated, added Deligne letter, original numbering retained.

Abstract

This is the article:

Deligne, P., and Milne, J.S., Tannakian Categories, in Hodge Cycles, Motives, and Shimura Varieties, LNM 900, 1982, pp. 101-228.

The 2012 version is a corrected TeXed version of the original. In the 2018 version, later results of Deligne has been incorporated into the text. There are only minimal changes from the original.

Contents

1. Tensor categories.
2. Neutral Tannakian categories.
3. Fibre functors; the general notion of a Tannakian category.
4. Polarizations.
5. Graded Tannakian categories.
6. Motives for absolute Hodge cycles
   Appendix: Terminology from nonabelian cohomology.
   Letter of Deligne, November 30 2011.

Thanks

For help with corrections: Peng DU; Enis Kaya; Parul Keshari; Kapil Paranjape; Julian Rosen.