Holonomic étale sheaves are constructible

Abstract

Building on Beilinson's work, ``constructible sheaves are holonomic,'' we introduce the notion of holonomicity for étale sheaves, without assuming a priori constructibility. Over a perfect base field, we establish the converse of Beilinson's result, showing that holonomic sheaves are indeed constructible. This can be seen as an étale analogue of Kashiwara's theorem on holonomic ${\mathcal D}_X$-modules.