Periods and Nori Motives by Annette Huber & Stefan Müller-Stach

Author:Annette Huber & Stefan Müller-Stach
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

induces an isomorphism

We define the (v, w)-component of to be the image of under this isomorphism.

In order to show that this is a well-defined element of , we need to check that diagrams of the form

commute for all edges , in F. We factor

and check the factors separately.

Consider the diagram

The outer square commutes because a is a diagram endomorphism of . The top and bottom square commute by definition of . The left- and right-hand square commute by property (3), up to the same sign . Hence the middle square commutes without signs. The analogous diagram for commutes on the nose. Hence is well-defined.

We now want to compare the (v, w)-component to the (w, v)-component. Recall that there is a distinguished edge . Consider the diagram

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