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    • The fundamental group and extensions of motives of Jacobians of curves

      SUBHAM SARKAR RAMESH SREEKANTAN

      Research Article Volume 130 Published: 30 January 2020 Article ID 0018

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

    • Keywords

       

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

    • Abstract

       

      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.

    • Author Affiliations

       

      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

    • Dates

       
      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

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