nLab Nori motive


under construction



Madhav Nori invented an original approach to mixed motives, in the spirit of Tannakian theory, but based on a specific Nori's Tannakian theorem. Unfortunately his original work, which has been lectured on some summer schools and conferences is not widely available in written form. Maxim Kontsevich based his approach to periods and their appearance in deformation quantization partly on Nori’s insight.

The construction of Nori motives themselves has been generalised to categories over a base S by Arapura and Ivorra. Arapura’s approach is based on constructible sheaves. His categories allow pull-back and push- forward, the latter being a deep result. The same paper also constructs the weight filtration on Nori motives and establishes the equivalence between Nori motives and André pure motives. Ivorra’s approach is based on perverse sheaves. Compatibility under the six functors formalism? is open in his setting [Huber-Stach]

It is known that Nori’s and Ayoub’s Motivic galois groups agree.

The subcategory of 1-motives in Nori motives agrees with Deligne’s 1-motives, and hence also with 1-motives in Voevodsky’s category.


Nori motives over a base S

Characterization of the universality of Nori motives via Barr completion of the syntactic category of the theory (in the formal logical sense) of singular cohomology of schemes is in

For more on this topos theory perspective, see

Last revised on March 8, 2019 at 14:17:01. See the history of this page for a list of all contributions to it.