Click here to view fulltext PDF

Permanent link:
https://www.ias.ac.in/article/fulltext/pmsc/130/0018

Algebraic cycles; mixed Hodge structures; extensions; regulators; curves; Jacobians; higher Chow cycles; motivic cycles

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.

SUBHAM SARKAR¹ RAMESH SREEKANTAN²

1. School of Mathematics, Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Colaba, Mumbai 400 005, India
2. Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Jnanabharathi, Bengaluru 560 059, India

Published

30 January 2020

Manuscript received

6 September 2018

Manuscript revised

21 May 2019

Accepted

29 May 2019

Early published

Unedited version published online

Final version published online

25 January 2020