In this paper, we construct extensions of mixed Hodge structure coming from the mixed Hodge structure on the graded quotients of the group ring of the fundamental group of a smooth projective pointed curve which correspond to the regulators of certain motivic cohomology cycles on the Jacobian of the curve essentially constructed by Bloch and Beilinson. This leads to a new iterated integral expression for the regulator. This is a generalisation of a theorem of Colombo (J. Algebr. Geom. 11(4) (2002) 761–790) where she constructed the extension corresponding to Collino’s cycles in the Jacobian of a hyperelliptic curve.
Volume 131, 2021
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