ALGEBRAIC DE RHAM THEORY FOR THE RELATIVE COMPLETION OF SL2(Z)

作者：Luo, M. A.^*

来源：Transactions of the American Mathematical Society, 2023.

DOI：10.1090/tran/9014

• Relative completion
• periods
• modular forms
• iterated integrals

We develop an explicit algebraic de Rham theory for the rela-tive completion of SL2(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 val-ues' defined by Brown.