Séminaire d'arithmétique à Lyon

Arithmetic group cohomology with generalised coefficients

by Dr Jun Su


Cohomology of arithmetic subgroups, with algebraic representations as coefficients, has played an important role in the construction of Langlands correspondence. Traditionally the first step to access these objects is to view them as cohomology of sheaves on locally symmetric spaces and hence connect them with spaces of functions. However, sometimes infinite dimensional coefficents also naturally arise, e.g. when you try to attach elliptic curves to weight 2 eigenforms on GL_2/an imaginary cubic field, and the sheaf theoretic viewpoint might no longer be fruitful. In this talk we'll explain a very simple alternative understanding of the connection between arithmetic group cohomology (with finite dimensional coefficients) and function spaces, and discuss its application to infinite dimensional coefficients.