Cohomology of Complex Torus Bundles Associated to Cocycles

[摘要] Equivariant holomorphic maps of Hermitian symmetric domains intoSiegel upper half spaces can be used to construct families ofabelian varieties parametrized by locally symmetric spaces, whichcan be regarded as complex torus bundles over the parameter spaces.We extend the construction of such torus bundles using 2-cocycles ofdiscrete subgroups of the semisimple Lie groups associated to thegiven symmetric domains and investigate some of their properties.In particular, we determine their cohomology along the fibers.

[学科分类] 数学（综合）