  Let $F$ be a non-Archimedean local field with residue field $k$ of odd
characteristic, and let $B/F$ be the division algebra of rank 4. We explicitly
construct a stable curve $\mathfrak{X}$ over the algebraic closure of $k$
admitting an action of $GL_2(F)\times B^\times \times W_F$ which realizes the
Jacquet-Langlands correspondence and the local Langlands correspondence in its
cohomology.
