3/11/2008

B. Gross
Harvard University

Arithmetic invariants of discrete Langlands parameters

Let G be a reductive algebraic group over a local field k. Hiraga, Ichino and Ikeda have recently proposed a general conjecture for the formal degree of a discrete series representation of G(k), using special values of the adjoint L-function and epsilon factor of its (conjectural) Langlands parameter. I will reformulate this conjecture using Euler-Poincare measure on G(k) and the motive of G, establish a key rationality property of the ratio of special values in the non-Archimedean case, and explore some of its implications for supercuspidal parameters. This is joint work with Mark Reeder.