Local Constants for Heisenberg Representations
Abstract
We can attach a local constant to every finite dimensional continuous complex representation of a local Galois group of a nonarchimedean local field $F/\mathbb{Q}_p$ by Deligne and Langlands. Tate \cite{JT1} gives an explicit formula for computing local constants for linear characters of $F^\times$, but there is no explicit formula of local constant for any arbitrary representation of a local Galois group. In this article we study Heisenberg representations of the absolute Galois group $G_F$ of $F$ and give invariant formulas of local constants for Heisenberg representations of dimension prime to $p$.
 Publication:

arXiv eprints
 Pub Date:
 January 2014
 arXiv:
 arXiv:1401.5449
 Bibcode:
 2014arXiv1401.5449B
 Keywords:

 Mathematics  Number Theory
 EPrint:
 p. 46. The object of this paper is the same as the first draft. Expect a few parts (in section 2), this paper is different from the first draft