Abstract: A fundamental operation in the smooth representation theory of a p-adic group G is parabolic induction. This allows one to construct smooth representations of G in terms of smooth representations of a proper Levi M, in a way that is known to preserve basic finiteness properties such as finite generation and admissibility. In this talk, we will discuss how to prove the analogues of these properties in the context of the geometrization of the local Langlands correspondence. In particular, we replace parabolic induction by a geometric Eisenstein functor which takes \ell-adic sheaves on the moduli stack of M-bundles on the Fargues-Fontaine curve to \ell-adic sheaves on the moduli stack of G-bundles, and show that this functor preserves compact and ULA sheaves, the geometric analogues of finitely generated and admissible representations, respectively. This is based on joint work with David Hansen and Peter Scholze.