Speaker: Prof. Loic Merel (University Paris-Cité)

Title: Artin motives and the Eisenstein Ideal

Time: 14:00-15:00  June 18, 2026 (Thursday)

Place: MCM110

Abstract: In 1979, Mazur twisted his Eisenstein quotient (of level N) by an odd Dirichlet character to make progress on the Birch and Swinnerton-Dyer conjecture at the Eisenstein primes. We consider a similar twist by any Artin motive ρ. We introduce  the winding element attached to ρ. It belongs to a certain module over the Hecke algebra T which acts on cusps forms of weight 2 for Γ_0(N). This Hecke module is filtered by powers of the Eisenstein ideal of T. The position of the winding element with respect to its filtration would carry information of a non-archimedean nature on ρ similar to the Stark conjectures (class number type fomulas). This is based on a joint work with Emmanuel Lecouturier.