Speaker: Prof. Loic Merel，University Paris-Cité

Title: Artin motives and the Eisenstein Ideal

Language: Chinese

Time & Venue: 2026.06.18 14:00-15:00 MCM410

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.