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arXiv · 2211.00444

The fundamental group and extensions of motives of Jacobians of curves

Subham Sarkar·Ramesh Sreekantan
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Abstract

In this paper we construct extensions of mixed Hodge structures coming from the mixed Hodge structure on the graded quotients of the group ring of the fundamental group of a smooth, projective, pointed curve. These extensions correspond to the regulators of certain motivic cycles in the Jacobian of the curve which were constructed by Beilinson and Bloch. This leads to a new iterated integral expression for the regulator. This is a generalisation of a theorem of Colombo where she constructed the extension corresponding to Collino's cycles in the Jacobian of a hyperelliptic curve.

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Subham Sarkar, Ramesh Sreekantan. 2022-11-01. The fundamental group and extensions of motives of Jacobians of curves. https://doi.org/10.1007/s12044-019-0539-z

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