Deligne--Langlands gamma factors in families

Abstract

Let F be a p-adic field, W_F its absolute Weil group, and let k be an algebraically closed field of prime characteristic l different from p. Attached to any l-adic representation of W_F are local epsilon- and L-factors. There are natural notions of families of l-adic representations of W_F, such as the theory of Galois deformations or, more generally, families over arbitrary Noetherian W(k)-algebras. However, the epsilon and L-factors do not interpolate well in such families. In this paper it is shown that the gamma factor, which is the product of the epsilon factor with a ratio of L-factors, interpolates over such families.

16 pages. New title, re-written for clarity and readability, corrections made in what is now section 2, and throughout

References in corpus (1)

• Whittaker models and the integral Bernstein center for GL_n

Cited by in corpus (5)

• Local Langlands correspondence, local factors, and zeta integrals in analytic families
• Converse theorems and the local Langlands correspondence in families
• The $\ell$-modular local Langlands correspondence and local factors
• On the local converse theorem and the descent theorem in families
• Characterizing the mod-$\ell$ local Langlands correspondence by nilpotent gamma factors