Papers by Brian Hwang

We give a proof of the Kronecker–Weber theorem using the deformation theory of one-dimensional Galois representations associated with algebraic Hecke characters and corresponding "level-lowering" and "modularity lifting" theorems for such representations.

We show that local models of Shimura varieties attached to "unramified Type A" data (relating to integral models of certain unitary Shimura varieties with parahoric level structure at a given place) coincide with a certain class of moduli spaces that arise in the theory of limit linear series over algebraic curves introduced by Osserman, called a linked Grassmannian. Roughly speaking, it shows that the infinitesimal variation in certain abelian varieties with level structure (or equivalently, their p-divisible groups) coincide with the variation seen in this moduli space of degenerating line bundles on certain reducible algebraic curves.

There is a curious "parity-switching" phenomenon that occurs when you apply the Jacquet-Langlands and local Langlands correspondence to a self-dual smooth, admissible representation of GL(n). Here, we give a geometric interpretation of this fact using the cohomology of the Lubin-Tate tower and provide a "calculus of signs" for determining the symplectic/orthogonal alternative.

We prove a simultaneous globalization or interpolation theorem for self-dual representations of GL(n) over a totally real number field at finitely many prescribed places, without making recourse to black-box results like Langlands functorial transfer from automorphic representations on classical groups to GL(n) or the stabilization of the twisted trace formula. The resulting cuspidal automorphic representations are cohomological, and so all of them have associated Galois representations.