Frederick Thogersen: Anti-cyclotomic p-adic L-functions for U(2n)

Number Theory Seminar: Frederick Thogersen (University of Nottingham)

Anti-cyclotomic p-adic L-functions for U(2n)

I will report on progress towards the construction of anti-cyclotomic p-adic L-functions for the definite unitary group of signature 2n over CM fields in two cases: finite slope and Coleman families. In this talk, I will explain how the construction p-adic L-functions via overconvergent cohomology unfolds and how this case has a particularly explicit construction with Gross algebraic modular forms. I’ll further seek to highlight key assumptions and limitations of current results with respect to required test vectors.