nLab Catégories Tannakiennes

This entry is about the article

on Tannakian categories.

The main theorem is a Tannakian reconstruction theorem, which repairs a problem in the work of Grothendieck’s student Saavedra Rivano:

  • Neantro Saavedra Rivano, Catégories Tannakiennes, Bulletin de la Société Mathématique de France 100 (1972) 417-430 [eudml:87193]

  • Neantro Saavedra Rivano, Catégories Tannakiennes, Springer LNM 265, 1972.

which had a substantial gap in the proof of the main theorem.

At the end of the article there is an application to the differential Galois theory (which has been earlier much studied by A. R. Magid) which is the Galois theory for differential rather than algebraic equations.

The article had a huge influence not only in Tannakian theory but also in creating more interactions between modern algebraic geometry, category theory, and the theory of bialgebras.

In the followup

  • Pierre Deligne, Catégorie Tensorielle, Moscow Math. Journal 2 (2002) no. 2, 227-248. (pdf)

the conditions for Tannakian reconstruction are relaxed further, see at Deligne's theorem on tensor categories.

A generalization to “non-neutral” Tannakian categories, and representations of gerbes is in

See also

category: reference

Last revised on August 23, 2023 at 05:24:38. See the history of this page for a list of all contributions to it.