Automorphic L-invariants for reductive groups

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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.