Bloch group

Recently I was trying to understand what’s behind the mysterious condition

for elements () to define an element in the Bloch group. It appears that the condition naturally appears if one studies hyperbolic -manifolds.

Tannakian categories

Of late, a lot of people have been asking me about Tannakian categories, so I decided to post this short blurb (mainly to check the Latex-related features of wordpress and also to provide some bird’s-eye view of why we should care about Tannakian categories.)

To begin with:

Definition
A neutral Tannakian category over a base field is a rigid abelian tensor category with an -linear exact faithful tensor ( being the category of vector spaces over ) which one calls the fiber functor.