EVENT DETAILS AND ABSTRACT

Title: Non-abelian local class field theory and the Lubin-Tate tower
Speaker: Jared Weinstein
Speaker Info: UCLA
Brief Description:
Special Note:
Abstract:

What are the algebraic extensions of a nonarchmidean local field (eg the p-adic numbers)? All of the abelian extensions of a nonarchimedean local field can be constructed by adjoining the torsion points of a one-dimensional formal module of height one: This is the crux of classical Lubin-Tate theory. The question of constructing the nonabelian extensions leads one to the study of the Lubin-Tate tower, which is a moduli space for deformations of formal modules of greater height. By results of Harris-Taylor and Boyer, the cohomology of the Lubin-Tate tower encodes precise information about non-abelian extensions of the local field (namely, it realizes the local Langlands correspondence). The Lubin-Tate tower has a horribly singular special fiber, which hinders any direct study of its cohomology, but we will show that after base extension there is a model for the tower whose reduction contains a very curious nonsingular hypersurface defined over a finite field. We will write down the equation for this hypersurface and then beg the audience for help in computing its zeta function.