Riemann-Roch for function fields via Fourier analysis

Ryan Rosenbaum, CU Boulder
Abstract : Tate included in his thesis an analog of Poisson summation on the adeles which he referred to as "Riemann-Roch" for number fields.  Our goal is to explain Tate's justification for using this name.  We will briefly review necessary properties of local and global fields along with the Fourier transform.  We will then introduce the notion of the divisor group for a function field and show that that Tate's "Riemann-Roch" implies a more familiar statement of theorem in this context.