Colocalization and cotilting for commutative noetherian rings.

Abstract: For a commutative noetherian ring R, we investigate relations between tilting and cotilting modules in and , where runs over the maximal spectrum of R. For each , we construct a correspondence between (equivalence classes of) n-cotilting R-modules C and (equivalence classes of) compatible families of n-cotilting -modules ( ). It is induced by the assignment , where is the colocalization of C at , and its inverse . We construct a similar correspondence for n-tilting modules using compatible families of localizations; however, there is no explicit formula for the inverse. [Copyright &y& Elsevier]