Martí Roset Julià

Rigid classes for SL(n) and their values at special points

The theory of complex multiplication implies that the values of modular functions at CM points belong to abelian extensions of imaginary quadratic fields. In this talk, we propose a conjectural extension of this phenomenon to the setting of totally real fields. Generalizing the work of Darmon, Pozzi, and Vonk, we construct rigid cocycles for SL(n), which play the role of modular functions, and define their values at points associated with totally real fields. The construction of these cocycles originates from a topological source: the Eisenstein class of a torus bundle. This is ongoing joint work with Peter Xu.