Conductors in $p$-adic families

Abstract

Given a Weil-Deligne representation of the Weil group of an $\ell$-adic number field with coefficients in a domain $\mathcal{O}$, we show that its pure specializations have the same conductor. More generally, we prove that the conductors of a collection of pure representations are equal if they lift to Weil-Deligne representations over domains containing $\mathcal{O}$ and the traces of these lifts are parametrized by a pseudorepresentation over $\mathcal{O}$.

arXiv admin note: text overlap with arXiv:1410.3843

References in corpus (1)

• Local-global compatibility and the action of monodromy on nearby cycles