Seminar in Algebraic Geometry and Number Theory / Half-way seminar

Abstract: Let F be a CM field and g an automorphic form of PGL(2,F). A conjecture of Venkatesh describes the structure of the contribution of g to the singular homology with rational coefficients of the locally symmetric spaces associated to PGL(2,F). I will introduce this conjecture and the main ingredients of my conditional proof of its p-adic realisation, wherein the coefficents are p-adic instead of rational.