The fundamental group and extensions of motives of Jacobians of curves

被引：0
作者：
Subham Sarkar
Ramesh Sreekantan
机构：
[1] Tata Institute of Fundamental Research,School of Mathematics
[2] Indian Statistical Institute,Statistics and Mathematics Unit
来源：
Proceedings - Mathematical Sciences | 2020年 / 130卷
关键词：
Algebraic cycles; mixed Hodge structures; extensions; regulators; curves; Jacobians; higher Chow cycles; motivic cycles; 19F27; 11G55; 14C30; 14C35;
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摘要：
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.
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