Vol. 13, No. 10, 2019

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The elliptic KZB connection and algebraic de Rham theory for unipotent fundamental groups of elliptic curves

Ma Luo

Vol. 13 (2019), No. 10, 2243–2275
Abstract

We develop an algebraic de Rham theory for unipotent fundamental groups of once punctured elliptic curves over a field of characteristic zero using the universal elliptic KZB connection of Calaque, Enriquez and Etingof (2009) and Levin and Racinet (2007). We use it to give an explicit version of Tannaka duality for unipotent connections over an elliptic curve with a regular singular point at the identity.

Keywords
elliptic KZB connection, unipotent fundamental groups, algebraic de Rham theory
Mathematical Subject Classification 2010
Primary: 11G05
Secondary: 14F40, 32G34
Milestones
Received: 27 March 2018
Revised: 23 January 2019
Accepted: 12 July 2019
Published: 6 January 2020
Authors
Ma Luo
University of Oxford
United Kingdom