Monodromy of elliptic curve convolution, seven-point sheaves of $G_2$-type and motives of Beauville type

Benjamin Collas; Michael Dettweiler; Stefan Reiter; Will Sawin

Monodromy of elliptic curve convolution, seven-point sheaves of $G_2$-type and motives of Beauville type

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arxiv 1803.05883 v2 pith:PRIIKWZ3 submitted 2018-03-15 math.AG

Benjamin Collas , Michael Dettweiler , Stefan Reiter , Will Sawin This is my paper · ORCID

classification math.AG

keywords monodromysheavesbeauvilleconvolutionellipticmotivestypeapproach

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abstract

We study the Tannakian properties of the category of perverse sheaves on elliptic curves endowed with the convolution product. We establish that for certain sheaves with unipotent local monodromy over seven points the corresponding Tannaka group is isomorphic to $G_2$. This monodromy approach generalizes a result of Katz on the existence of $G_2$-motives in the middle cohomology of deformations of Beauville surfaces.

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