  We consider Lie algebroids over an algebraic space (or topological ringed
space) as quasicoherent sheaves of Lie-Rinehart algebras. We express
hypercohomology for a locally free Lie algebroid (not necessarily of finite
rank) as a derived functor, and simplify it via \v{C}ech cohomology.
Furthermore, we define the Hochschild hypercohomology of a sheaf of generalized
bialgebras and study the cases of the universal enveloping algebroid and the
jet algebroid of a Lie algebroid. In the sequel, we present a version of
Hochschild-Kostant-Rosenberg theorem for a locally free Lie algebroid, as well
as its dual version.
