$\Lambda$-adic Families of Jacobi Forms.

We show that Hida theory of ordinary $p$-adic families of elliptic cuspforms extends to $p$-adic families of Jacobi forms. We also construct $p$-adic versions of theta lifts from elliptic modular forms to Jacobi forms. Our results extend to Jacobi forms previous works by Hida and Stevens on the related case of half-integral weight modular forms.