论文标题
Shimura品种，动机共同体和Archimedean $ L $ -PACKETS的相干共同学
Coherent cohomology of Shimura varieties, motivic cohomology, and archimedean $L$-packets
论文作者
论文摘要
我们制定了prasanna-venkatesh的阿基米德动机动作动作的类似物，用于shimura品种上不规则的同型体型形式，这些形式出现在多个程度的Shimura品种的相干共同体上。这样的多个出现是由于单个$ l $ - 包装中的无限类型，具有相等的$ k $ types。因此，我们制定了猜想的比较，以比较不同自动形态表示形式的时期。我们通过在自动形式时期显示出与现有猜想的兼容性来提供猜想的证据。这些猜想表明存在某些操作，这些操作在$ l $ - 包装中的不同无限类型之间移动。
We formulate an analogue of the archimedean motivic action conjecture of Prasanna--Venkatesh for irregular cohomological automorphic forms on Shimura varieties, which appear on multiple degrees of coherent cohomology of Shimura varieties. Such multiple appearances are due to many infinity types in a single $L$-packet with equal minimal $K$-types. Accordingly, we formulate the conjecture comparing periods of forms of different automorphic representations. We provide evidences for the conjecture by showing its compatibility with existing conjectures on periods of automorphic forms. The conjectures suggest the existence of certain operations which move between different infinity types in an $L$-packet.
