Monodromy of elliptic curve convolution, seven-point sheaves of <i>G</i> <sub>2</sub> type, and motives of Beauville type-Reference-Cited by-同舟云学术

Monodromy of elliptic curve convolution, seven-point sheaves of G ₂ type, and motives of Beauville type

Published:2022-01-23 Issue:784 Volume:2022 Page:1-26
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Collas Benjamin¹,Dettweiler Michael¹,Reiter Stefan¹,Sawin Will²^ORCID

Affiliation:

1. Department of Mathematics , Universität Bayreuth , 95440 , Bayreuth , Germany

2. Department of Mathematics , Columbia University , 10027 New York , NY , USA

Abstract

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 G 2

{G_{2}}

. This monodromy approach generalizes a result of Katz on the existence of G 2

{G_{2}}

-motives in the middle cohomology of deformations of Beauville surfaces.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2021-0070/pdf

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