Goresky-Pardon extensions of Chern classes and associated Tate extensions
Goresky-Pardon extensions of Chern classes and associated Tate extensions
复制标题
Chern 类的 Goresky-Pardon 扩展和相关的 Tate 扩展
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
E. Looijenga
中科院分区：
文献类型：
--
作者：
E. Looijenga
设X是不可约复簇，S是X的分层，F是开状态上的全纯向量丛。我们给出了S和F上的几何条件，使得第k个陈类F是X的复上同调中Hodge水平至少为k的一类的自然扩张。当X是一个局部对称簇的Baily-Borel紧化，它的分层由边界分量，和F的自守丛在其内部，那么这恢复和改进的Goresky-Pardon定理。通过定义Baily-Borel紧化的一类单纯分解，可以用来定义它的混合Hodge结构。最后，我们利用有理数的Beilinson调节子证明了当X是A_g的Satake（=Baily-Borel）紧化，F是Hodge丛（g大于k）时，Goresky-Pardon第k次Chern类扩张的虚部不为零，并产生一个基本Tate扩张.
Let X be an irreducible complex variety, S a stratification of X and F a holomorphic vector bundle on the open statum. We give geometric conditions on S and F that produce a natural extension of the k-th Chern class F as a class in the complex cohomology of X of Hodge level at least k. When X is the Baily-Borel compactification of a locally symmetric variety with its stratification by boundary components, and F an automorphic bundle on its interior, then this recovers and refines a theorem of Goresky-Pardon. In passing we define a class of simplicial resolutions of the Baily-Borel compactification that can be used to define its mixed Hodge structure. Finally, we use the Beilinson regulator for the rationals to show that when X is the Satake (=Baily-Borel) compactification of A_g and F the Hodge bundle (with g large compared to k), the Goresky-Pardon k-th Chern class extension has nonzero imaginary part and gives rise to a basic Tate extension.
影响因子：
0.7
作者：
Esnault, Hélène;Harris, Michael
通讯作者：
Harris, Michael