NUmber Theory Seminar 2025

During semester 1, we will meet on Mondays at 11am in Peter Hall 162. Here is an (incomplete) list of references for algebraic modular forms.

Algebraic modular forms; elliptic curve isogeny graphs

22 January 2025, at 11am in Peter Hall 162: Relative completed cohomologies and modular symbols, by Dongwen Liu (Zhejiang University).
Abstract: Generalizing Emerton's completed cohomologies, we define relative completed cohomologies of arithmetic manifolds and their modular symbols, which interpolate the nearly ordinary part of the classical automorphic cohomologies and classical modular symbols. As applications, we construct three families of nearly ordinary p-adic L-functions. The modifying factors at infinity are consistent with the conjectures given by Deligne and Blasius, and the modifying factors at p are consistent with the conjecture given by Coates and Perrin-Riou. This is a joint work with Binyong Sun.
28 January 2025, at 11am in Peter Hall 162: Integral Sen theory and integral Hodge filtration, by Hui Gao (SUSTech).
Abstract: Using the Breuil–Kisin module attached to an integral crystalline representation, one can define an integral Hodge filtration whose behavior is closely related to arithmetic and geometry of the representation. In this talk, we discuss vanishing and torsion bound on graded pieces of this filtration, using a filtered integral Sen theory as key tool. This is joint work with Tong Liu.