Cohomology of algebraic varieties / Cohomologie des variétés algébriques

Collection Cohomology of algebraic varieties / Cohomologie des variétés algébriques

Organizer(s) Cadoret, Anna ; Charles, François ; Demarche, Cyril ; Klingler, Bruno ; Moonen, Ben

Date(s) 15/10/2018 - 19/10/2018

linked URL https://conferences.cirm-math.fr/1775.html

00:00:00 / 00:00:00

1 6

Symmetric power moments of Kloosterman sums

By Javier Fresán

We construct motives over the rational numbers associated with symmetric power moments of Kloosterman sums, and prove that their $L$-functions extend meromorphically to the complex plane and satisfy a functional equation conjectured by Broadhurst and Roberts. Although the motives in question turn out to be classical, the strategy consists in first realizing them as exponential motives and computing their Hodge numbers by means of the irregular Hodge filtration. We show that all Hodge numbers are either zero or one, which implies potential automorphicity thanks to recent results of Patrikis and Taylor. The first talk will be concerned with the arithmetic aspects and in the second one we will present the Hodge theoretic computations. Joint work with Claude Sabbah and Jeng-Daw Yu.

Information about the video

Date of recording 15/10/2018
Date of publication 25/10/2018
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19466903
Cite this video Fresán, Javier (15/10/2018). Symmetric power moments of Kloosterman sums. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19466903
URL https://dx.doi.org/10.24350/CIRM.V.19466903

Domain(s)

Bibliography

Fresán, J., Sabbah, C., & Yu, J.-D. (2018). Hodge theory of Kloosterman connections. <arXiv:1810.06454> - https://arxiv.org/abs/1810.06454

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