Norm-compatible systems of cohomology classes for
arXiv:1711.10571
Abstract
We describe work of Faltings on the construction of étale cohomology classes associated to symplectic Shimura varieties and show that they satisfy certain trace compatibilities similar to the ones of Siegel units in the modular curve case. Starting from those, we construct a two variable family of trace-compatible classes in the cohomology of a unitary Shimura variety.
33 pages; title changed; in the current version, we construct a two variable family of norm-compatible classes in the cohomology of the Shimura variety for GU(2,2) (see Theorem B of the introduction), improving substantially Corollary B of the previous version