English

Deligne--Langlands gamma factors in families

Number Theory 2017-08-11 v3

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.

Keywords

Cite

@article{arxiv.1510.08743,
  title  = {Deligne--Langlands gamma factors in families},
  author = {David Helm and Gilbert Moss},
  journal= {arXiv preprint arXiv:1510.08743},
  year   = {2017}
}

Comments

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