论文标题
Eisenstein Cycles和Manin Drinfeld特性
The Eisenstein cycles and Manin Drinfeld properties
论文作者
论文摘要
考虑模块化组有限指数的亚组。我们给出了尖尖的分裂的分析标准，是相应模块化曲线的雅各布式的扭转。通过Belyi定理，此类标准将适用于数字字段上的任何曲线。我们的主要工具是根据模块化符号的明确描述我们所谓的爱森斯坦周期。后者是相对同源类别的表示，在这些类别的整合中，任何骨膜差异形式的整合都消失了。我们的方法在特定情况下以一种重要的方式依赖，我们可以考虑方便的广义雅各布人而不是雅各比亚人。 Eisenstein类是具有复杂系数的某些同源类别的实际部分。这些类别的假想部分与爱森斯坦系列的散射常数有关。最后，我们通过考虑Fermat曲线来说明我们的理论。
Consider a subgroup of finite index of modular group. We give an analytic criterion for a cuspidal divisor to be torsion in the Jacobian of the corresponding modular curve. By BelyI theorem, such a criterion would apply to any curve over a number field. Our main tool is the explicit description, in terms of modular symbols, of what we call Eisenstein cycles. The latter are representations of relative homology classes over which integration of any holomorphic differential forms vanishes. Our approach relies in an essential way on the specific case , where we can consider convenient generalized Jacobians instead of Jacobian. The Eisenstein classes are the real part of certain homology classes with complex coefficients. The imaginary part of those classes are related to the scattering constants attached to Eisenstein series. Finally, we illustrate our theory by considering Fermat curves.
