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arXiv · 1510.08743

Deligne--Langlands gamma factors in families

David Helm·Gilbert Moss
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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.

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David Helm, Gilbert Moss. 2017-08-09. Deligne--Langlands gamma factors in families. https://arxiv.org/abs/1510.08743

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