Comptes Rendus
no. 3
Number theory/Algebraic geometry
On Deligne's periods for tensor product motives

Presented by: Claire Voisin

Chandrasheel Bhagwat1
1 Indian 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 
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.11.016/

[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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