Subham Sarkar, Ramesh Sreekantan
Published 2014-06-03, updated 2017-03-30Version 2
In this paper we construct extensions of the Mixed Hodge structure on the fundamental group of a pointed algebraic curve. These extensions correspond to the regulator of certain explicit motivic cohomology cycles in the self product of the curve which were first constructed by Bloch and Beilinson. This leads to a new iterated integral expression for the regulator. Our result is a generalization of a result of Colombo's where she constructs the extension corresponding to a motivic cycle class in the Jacobian of a hyperelliptic curve constructed by Collino. This is to appear in the Mathematical Proceedings of the Indian Academy of Sciences.
The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles
The Mixed Hodge Structure on the Fundamental Group of a Punctured Riemann Surface
Weighted Completion of Galois Groups and Galois Actions on the Fundamental Group of P^1 - {0,1,infinity}
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