论文标题
希尔伯特·艾森斯坦（Hilbert Eisenstein）系列的非理性时期通过环形紧凑
Irrational periods of Hilbert Eisenstein series via toroidal compactification
论文作者
论文摘要
我们表明，希尔伯特模块化表面上的1级平行重量2（平行重量2）的周期也不是理性的，即使缩放也是如此。这是从对希尔伯特模块化表面的共同体的混合霍奇结构的研究中得出的，在那里我们发现与实际二次场单位相关的扩展类别。我们证明了所有维度的Hilbert模块化变种的结果，并在odletale的共同体中产生了Galois表示的扩展。关键点是研究霍奇束的规范延伸到光滑的环形紧凑型边界的限制。
We show that the periods of the holomorphic Eisenstein series of level 1, parallel weight 2, on a Hilbert modular surface are not rational, even up to scaling. This is deduced from a study of the mixed Hodge structure on the cohomology of the Hilbert modular surface, where we find extension classes related to the units of the real quadratic field. We prove similar results for Hilbert modular varieties of all dimensions, and produce extensions of Galois representations in étale cohomology. The key point is to study the restriction of the canonical extension of the Hodge bundle to the boundary of a smooth toroidal compactification.
