论文标题
艾森斯坦共同体中的共同体
Eisenstein cocycles in motivic cohomology
论文作者
论文摘要
几位作者研究了从模块化曲线的第一个同源组到循环环形环或模块化曲线X的第二个K组的同态性。这些地图将同源性组中的Manin符号发送到Steinberg cyclotomic或siegel单位的符号。我们提供了这些地图的新结构，并直接证明了它们的Hecke均等性，类似于使用通用椭圆曲线构建Siegel单元。我们的主要工具是一个从GL_2（Z）到X上合适组方案的函数场的第二个K组的1循环，从中出现了感兴趣的图。
Several authors have studied homomorphisms from first homology groups of modular curves to the second K-group of a cyclotomic ring or a modular curve X. These maps send Manin symbols in the homology groups to Steinberg symbols of cyclotomic or Siegel units. We give a new construction of these maps and a direct proof of their Hecke equivariance, analogous to the construction of Siegel units using the universal elliptic curve. Our main tool is a 1-cocycle from GL_2(Z) to the second K-group of the function field of a suitable group scheme over X, from which the maps of interest arise by specialization.
