Constructible sheaves on schemes

We present a uniform theory of constructible sheaves on arbitrary schemes with coefficients in topological or even condensed rings. This is accomplished by defining lisse sheaves to be the dualizable objects in the derived & INFIN;-category of proetale sheaves, while constructible sheaves are those that are lisse on a stratification. We show that constructible sheaves satisfy proetale descent. We also establish a t-structure on constructible sheaves in a wide range of cases. We finally provide a toolset to manipulate categories of constructible sheaves with respect to the choices of coefficient rings, and use this to prove that our notions reproduce and extend the various approaches to, say, constructible 8-adic sheaves in the literature.& COPY; 2023 Elsevier Inc. All rights reserved.