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

Luo, Ma

doi:10.2140/ant.2019.13.2243

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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

DOI: 10.2140/ant.2019.13.2243

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.

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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

Vol. 13, No. 10, 2019