Monodromy of elliptic curve convolution, seven-point sheaves of G₂-type, and motives of Beauville type

Titelangaben

Collas, Benjamin ; Dettweiler, Michael ; Reiter, Stefan ; Sawin, Will:
Monodromy of elliptic curve convolution, seven-point sheaves of G₂-type, and motives of Beauville type.
In: Journal für die Reine und Angewandte Mathematik. (2022) Heft 784 . - S. 1-26.
ISSN 1435-5345
DOI: https://doi.org/10.1515/crelle-2021-0070

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Abstract

We study Tannakian properties of the convolution product of perverse sheaves on elliptic curves. We establish that for certain sheaves with unipotent local monodromy over seven points the corresponding Tannaka group is isomorphic to G2. This monodromy approach generalizes a result of Katz on the existence of G2-motives in the middle cohomology of deformations of Beauville surfaces.