Conductors in $p$-adic families

Jyoti Prakash Saha

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arXiv · 1512.03004

Conductors in $p$-adic families

Jyoti Prakash Saha

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Abstract

Given a Weil-Deligne representation of the Weil group of an $\ell$-adic number field with coefficients in a domain $\mathscr{O}$, 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 $\mathscr{O}$ and the traces of these lifts are parametrized by a pseudorepresentation over $\mathscr{O}$.

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Jyoti Prakash Saha. 2015-12-04. Conductors in $p$-adic families. https://arxiv.org/abs/1512.03004

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