Derived equivalence induced by infinitely generated n-tilting modules

Let TR be a right n-tilting module over an arbitrary associative ring R. In this paper we prove that there exists an n-tilting module TR′ equiva- lent to TR which induces a derived equivalence between the unbounded derived category D(R) and a triangulated subcategory E⊥ of D(End(T′)) equivalent to the quotient category of D(End(T′)) modulo the kernel of the total left derived functor − ⊗LS′ T ′. If TR is a classical n-tilting module, we have that T = T ′ and the subcategory E⊥ coincides with D(End |(T )), recovering the classical case.