Nori-Motive und Tannaka-Theorie

TL;DR

This paper explains Nori's construction of a universal category of motives using diagram categories, proves its universal property, and explores its connections to Tannaka duality and affine group schemes.

Contribution

It formalizes Nori's diagram category construction, proves its universal property, and links it to Tannaka duality and affine group schemes.

Findings

Established criteria for the diagram category to be modules over a coalgebra

Proved the universal property of Nori's diagram category

Connected the diagram category to Tannaka duality and motives

Abstract

In the late 90s M. V. Nori constructed a category of motives in charakteristic 0. Using a directed graph with a representation into noetherian R-Modules, he defined a universal R-linear abelian category, called diagram category.The following paper describes this construction and gives proof to the necessary universal property. In addition we establish a criteria for the diagram category to be a category of finitely generated modules over a certain coalgebra. Finally we sketch the connection between the diagram category and the representations of affine group schemes (Tannaka-Dualism) and define the category of mixed Nori-Motives.