论文标题
曲线雅各布人的基本组和动机的扩展
The fundamental group and extensions of motives of Jacobians of curves
论文作者
论文摘要
在本文中，我们构建了来自混合霍奇结构的混合杂货结构的扩展，该结构来自混合的霍奇结构，这是在光滑，投射，尖曲线的基本组的组环上的分级环上。这些扩展对应于曲线的雅各布式中某些动机循环的调节因子，这些循环是由贝林森和布洛赫构建的。这导致了调节器的新迭代积分表达式。这是科伦坡定理的概括，在该定理中，她构建了与柯利诺循环相对应的延伸，在骨膜曲线的雅各布式中。
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.
