Algebraic de Rham theory for relative completion of ${\mathrm{SL}}_2(\mathbb{Z})$

Abstract

We develop an explicit algebriac de Rham theory for relative completion of ${\mathrm{SL}}_2(\mathbb{Z})$. This allows the construction of iterated integrals involving modular forms of the second kind, generalizing iterated integrals of holomorphic modular forms that were previously studied by Brown and Manin. These newly constructed iterated integrals provide all 'multiple modular values' defined by Brown.

arXiv commentRevised mostly the last 3 sections, updated introduction and references

References in corpus (4)

• Multiple Modular Values and the relative completion of the fundamental group of $M_{1,1}$
• Notes on the Universal Elliptic KZB Equation
• Algebraic de Rham theory for weakly holomorphic modular forms of level one
• The elliptic KZB connection and algebraic de Rham theory for unipotent fundamental groups of elliptic curves

Cited by in corpus (2)

• From the Deligne-Ihara conjecture to Multiple Modular Values
• Moduli of framed formal curves