This is a joint work with my teacher Changchang Xi. We discuss infinitely generated tilting
modules of higher projective dimension under the frame work of Ringel modules and in terms of derived
module categories. Sufficient and necessary conditions are given for the kernels of the left-derived
tensor functors induced by arbitrary tilting modules to be homological subcategories. Thus, Happel's theorem
for homological infinitely generated tilting modules takes a new fashion as recollements of derived module
categories. As a consequence, we find the first example of higher dimensional tilting modules, in which such
a recollement of derived module categories does not exist.
