Comptes Rendus
no. 3
Number theory/Algebraic geometry
On Deligne's periods for tensor product motives
Claire Voisin
Chandrasheel Bhagwat1
1Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune 411008, India
Comptes Rendus. Mathématique, Volume 353 (2015) no. 3, pp. 191-195

In this paper, we give a description of Deligne's periods c± for a tensor product of pure motives M⊗M′ over Q in terms of the period invariants attached to M and M′ by Yoshida [8]. The period relations proved by the author and Raghuram in an earlier paper follow from the results of this paper.

Nous décrivons dans cette Note les périodes de Deligne c± des produits tensoriels M⊗M′ de motifs purs sur Q, en termes des périodes des motifs M et M′ et des invariants qui leur sont attachés par Yoshida. Les relations de périodes établies antérieurement par l'auteur et Raghuram résultent de cette description.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.11.016

Chandrasheel Bhagwat  1

1 Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune 411008, India 
Chandrasheel Bhagwat. On Deligne's periods for tensor product motives. Comptes Rendus. Mathématique, Volume 353 (2015) no. 3, pp. 191-195. doi: 10.1016/j.crma.2014.11.016
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[1] C. Bhagwat; A. Raghuram Ratios of periods for tensor product motives, Math. Res. Lett., Volume 20 (2013) no. 4, pp. 615-628

[2] L. Clozel Motifs et formes automorphes: applications du principe de fonctorialité, Ann Arbor, MI, 1988 (L. Clozel; J.S. Milne, eds.) (Perspect. Math.), Volume vol. 10, Academic Press, Boston, MA (1990), pp. 77-159

[3] P. Deligne Valeurs de fonctions L et périodes d'intégrales, Proc. Sympos. Pure Math., vol. XXXIII, part II, American Mathematical Society, Providence, RI, USA, 1979, pp. 313-346 (With an appendix by N. Koblitz and A. Ogus)

[4] H. Grobner; M. Harris Whittaker periods, motivic periods, and special values of tensor product L-functions (Preprint, 2013, available at) | arXiv

[5] A. Raghuram On the special values of certain Rankin–Selberg L-functions and applications to odd symmetric power L-functions of modular forms, Int. Math. Res. Not. (2010), pp. 334-372 | DOI

[6] A. Raghuram, Critical values of Rankin–Selberg L-functions for GLn×GLn−1 and the symmetric cube L-functions for GL2, Preprint, 2014.

[7] A. Raghuram; F. Shahidi On certain period relations for cusp forms on GLn, Int. Math. Res. Not. (2008) | DOI

[8] H. Yoshida Motives and Siegel modular forms, Amer. J. Math., Volume 123 (2001), pp. 1171-1197

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