p-adic Fourier theory and p-adic L-functions for totally imaginary fields

par Johannes Sprang

jeudi 16 janv. 2025, 14:00 → 16:00 Europe/Paris

Since the pioneering work of Kubota and Leopoldt on the p-adic interpolation of (critical) Dirichlet L-values, this area of research has been significantly extended to more general number fields. Because critical Hecke L-values exist only for number fields that are either totally real or totally imaginary, the theory naturally divides into these two cases. Thanks to the contributions of Cassou-Noguès, Deligne-Ribet, and Barsky, we now have a good understanding of the totally real case. However, the totally imaginary case remains less well understood.
Under certain ordinariness assumptions, Katz successfully constructed p-adic L-functions for CM fields. For general (non-ordinary) primes, progress has been limited, with most results restricted to the case of imaginary quadratic fields. In this talk, I will present work in progress with Guido Kings on the construction of p-adic L-functions for totally real fields and discuss how this is connected to p-adic Fourier theory.