Monodromy of elliptic curve convolution, seven-point sheaves of G2type, and motives of Beauville type

Benjamin Collas; Michael Dettweiler; Stefan Reiter; Will Sawin

doi:10.1515/crelle-2021-0070

Monodromy of elliptic curve convolution, seven-point sheaves of G₂type, and motives of Beauville type

Benjamin Collas, Michael Dettweiler, Stefan Reiter, Will Sawin

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	1-26
Number of pages	26
Journal	Journal fur die Reine und Angewandte Mathematik
Volume	2022
Issue number	784
DOIs	https://doi.org/10.1515/crelle-2021-0070
State	Published - Mar 1 2022
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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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.",

author = "Benjamin Collas and Michael Dettweiler and Stefan Reiter and Will Sawin",

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AU - Dettweiler, Michael

AU - Reiter, Stefan

AU - Sawin, Will

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AB - 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.

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Monodromy of elliptic curve convolution, seven-point sheaves of G₂type, and motives of Beauville type

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