Computational Algebra Seminar: Combes -- Lifting ethereal Bianchi modular forms

Speaker: Lewis Combes (Sydney) 

Title: Lifting ethereal Bianchi modular forms 

Time & Place: 15:00-16:00, Thursday 8 Oct, SMRI Seminar Rm 

Abstract: The Bianchigroups--arithmetic groups like PSL(2,Z[i])--have many classes
appearing in mod p cohomology that don't lift to characteristic 0.  Such classes are
called etherealmodular forms, and their connections to modular forms in characteristic 0
remain somewhat mysterious.  In this talk we will cover recent work, joint with HÃ¥vard
Damm-Johnsen, concerning when and whether these forms can be lifted to characteristic 0
after passing to subgroups of higher level.  The aim of the project is to lift as many
mod p forms as we can; whether this can be done in general is unknown.  We present
proofs in some cases and evidence in others, that ethereal forms for Euclidean Bianchi
groups often have lifts to characteristic 0.