A family of irreducible supersingular representations of ${\mathrm{GL}}_2(F)$ for some ramified $p$-adic fields

Abstract

We construct infinite families of irreducible supersingular mod $p$ representations of ${\mathrm{GL}}_2(F)$ with ${\mathrm{GL}}_2({\mathcal{O}}_F)$-socle compatible with Serre's modularity conjecture, where $F/{\mathbb{Q}}_p$ is any finite extension with residue field ${\mathbb{F}}_{p^2}$ and ramification degree $e\le (p-1)/2$. These are the first such examples for ramified $F/{\mathbb{Q}}_p$.

Some typos corrected, to appear in Israel J. Math

References in corpus (1)

• Conjectures and results on modular representations of ${\mathrm{GL}}_n(K)$ for a $p$-adic field $K$