On Deligne's periods for tensor product motives

Abstract

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

arXiv comment6 pages, published in Comptes rendus - Mathématique in January 2015. Formerly appendix to arXiv1312.5955

References in corpus (2)

• Whittaker periods, motivic periods, and special values of tensor product L-functions
• Critical values of Rankin-Selberg L-functions for GL(n) x GL(n-1) and the symmetric cube L-functions for GL(2)

Cited by in corpus (5)

• Eisenstein Cohomology for GL(N) and ratios of critical values of Rankin-Selberg L-functions
• Critical values of Rankin-Selberg L-functions for GL(n) x GL(n-1) and the symmetric cube L-functions for GL(2)
• On Deligne's conjecture for certain automorphic $L$-functions for $\mathrm{GL}(3)\times \mathrm{GL}(2)$
• Algebraicity of the near central non-critical value of symmetric fourth $L$-functions for Hilbert modular forms
• Period relations between the Betti-Whittaker periods for ${\mathrm{GL}}_n$ under duality