Automorphic L-invariants for reductive groups

这个项目致力于构造和研究约化群的上同调、尖点自守表示的自守L-不变量。这些是p进数，它们是使用p算术群的上同调定义的。它们大概描述了局部p进伽罗瓦表示的约化，根据朗兰兹纲领，局部p进伽罗瓦表示与这种自守表示相关联。此外，L-不变量出现在特殊值公式中 本文首先定义了任意约化群的自守L-不变量，然后将它们与其它类型的L-不变量进行了比较，最后讨论了自守L-不变量的性质，并给出了自守L-不变量的定义。最后，研究了它们与p-adic L函数导数的关系。

This project is dedicated to the construction and study of automorphic L-invariants for cohomological, cuspidal automorphic representations of reductive groups.These are p-adic numbers, which are defined using the cohomology of p-arithmetic groups. They presumably describe the reducibility of local p-adic Galois representations, which, according to the Langlands program, are associated to such automorphic representations.In addition, L-invariants appear in special value formulas ​​of p-adic L functions in the case of exceptional zeros.The construction of automorphic L-invariants is known so far only in the case that the underlying group is the general linear group of degree 2.The goal of the project is first to define automorphic L-invariants for arbitrary reductive groups.Thereafter, they are compared with other types of L-invariants, which are defined in terms of completed cohomology or Galois representations.Finally, their relation to derivatives of p-adic L functions will be investigated.