On Deligne's periods for tensor product motives

TL;DR

This paper describes Deligne's periods for tensor product motives over Q using Yoshida's invariants, establishing period relations that connect the periods of individual motives to their tensor product.

Contribution

It provides a new description of Deligne's periods for tensor products of pure motives in terms of existing period invariants, extending previous period relation results.

Findings

Derived explicit formulas for Deligne's periods of tensor product motives.

Established period relations linking individual motives to their tensor products.

Connected period invariants with Yoshida's invariants for pure motives.

Abstract

In this paper, we give a description of Deligne's periods $c^\pm$ for tensor product of pure motives $M \otimes M'$ over $\mathbb{Q}$ in terms of the period invariants attached to $M$ and $M'$ by Yoshida. The period relations proved by the author and Raghuram in an earlier paper follow from the results of this paper.