发帖
雷达卡
摘要翻译：
本文的主要结果是Levin定义的电流在拓扑层次上给出了Abel格式的多对数的描述。这个结果是莱文的猜想。这提供了一种在拓扑层次上显式阿贝尔格式的Eisenstein类的方法。这些类是特别有趣的，因为它们有一个由国王定理产生的母题起源。在即将发表的一篇文章中，我们利用本文的主要结果，证明了Hilbert-Blumenthal簇上的泛Abel格式的Eisenstein类在Baily-Borel紧实的边界上退化，该Baily-Borel紧实的Baily-Borel紧实的Baily-Borel紧实的Baily-Borel紧实的Baily-Borel紧实的Baily-Borel紧实的Baily-Borel紧实的Baily-Borel紧实的Baily-Borel紧作为推论，在这种几何情形下，我们得到了其中一些Eisenstein类的非消失结果。
---
英文标题：
《Realisation de Hodge du polylogarithme d'un schema abelien》
---
作者：
David Blottiere (appendice d'Andrey Levin)
---
最新提交年份：
2008
---
分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--
---
英文摘要：
The main result of this article is the fact that the currents defined by Levin give a description of the polylogarithm of an abelian scheme at the topological level. This result was a conjecture of Levin. This provides a method to explicit the Eisenstein classes of an abelian scheme at the topological level. These classes are of special interest since they have a motivic origin by a theorem of Kings. In a forthcoming article, we use the main result of this paper to prove that the Eisenstein classes of the universal abelian scheme over an Hilbert-Blumenthal variety degenerate at the boundary of the Baily-Borel compactification of the base in a special value of an $L$-function associated to the underlying totally real number field. As a corollary, we get a non vanishing result for some of these Eisenstein classes in this geometric situation.
---
PDF链接：
https://arxiv.org/pdf/0705.0880
京公网安备 11010802022788号
