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

Author:

Collas Benjamin1,Dettweiler Michael1,Reiter Stefan1,Sawin Will2ORCID

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

Reference27 articles.

1. A. Beauville, Les familles stables de courbes elliptiques sur 𝐏1{\mathbf{P}}^{1} admettant quatre fibres singulières, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), no. 19, 657–660.

2. A. A. Beĭlinson, J. Bernstein and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy 1981), Astérisque 100, Société Mathématique de France, Paris (1982), 5–171.

3. P. Bellingeri, On presentations of surface braid groups, J. Algebra 274 (2004), no. 2, 543–563.

4. J. S. Birman, On braid groups, Comm. Pure Appl. Math. 22 (1969), 41–72.

5. J. S. Birman, Braids, links, and mapping class groups, Ann. of Math. Stud. 82, Princeton University, Princeton 1975.

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