Non-vanishing mod $p$ of derived Hecke algebras of multiplicative groups over number fields, II

Source abstract

We investigate the derived Hecke action on the cohomology of an arithmetic manifold associated to the multiplicative group over a number field. Under mild assumptions, we prove that the derived Hecke action is non-vanishing modulo $p$ in every degree. Moreover, the total cohomology ring with $\mathbb F_p$-coefficients is a free graded module of rank one over the derived Hecke algebra, generated in degree zero.