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

2018/03/15 by Benjamin Collas, Collas, Benjamin, Michael Dettweiler +5 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1803.05883

32 pages, including 12 figures and Magma code

arxiv created 2018/12/07 · arxiv updated 2018/12/10

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 G₂. This monodromy approach generalizes a result of Katz on the existence of G₂-motives in the middle cohomology of deformations of Beauville surfaces.

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