Real Regulators on Self-Products of K3 Surfaces

椭圆曲线乘积的实调节子

Real Regulators for Products of Elliptic Curves

本文在Kunneth分解假设下，证明了对足够多的椭圆曲线乘积，实调节子的Hodge-${\mathcal D}$-猜想不成立，给出了反例。

模形式Rankin-Selberg积的正则子

Regulators for Rankin-Selberg products of modular forms

该论文证明了两个模形式Rankin-Selberg积的L-函数非临界值上Beilinson猜想的一个弱版本。

A simple construction of indecomposable higher Chow cycles in elliptic surfaces

I construct regulator indecomposable higher Chow cycles in elliptic surfaces satisfying certain conditions. As an application I give an alternative proof of a theorem of Gordon and Lewis, which asserts that there is a real regulator indecomposable cycles in a product of general elliptic curves.

Extensions of Motives and the Fundamental Group

In this paper we construct extensions of the Mixed Hodge structure on the fundamental group of a pointed algebraic curve. These extensions correspond to the regulator of certain explicit motivic cohomology cycles in the self product of the curve which were first constructed by Bloch and Beilinson. This leads to a new iterated integral expression for the regulator. Our result is a generalization of a result of Colombo's where she constructs the extension corresponding to a motivic cycle class in the Jacobian of a hyperelliptic curve constructed by Collino. This is to appear in the Mathematical …