Publication at Faculty of Mathematics and Physics |
2014
Abstract
For a commutative noetherian ring R, we investigate relations between tilting and cotilting modules in Mod R and Mod R,, where in runs over the maximal spectrum of R. For each n (C-m vertical bar m is an element of mSpec(R)), where C-m = Hom(R)(R C) is the colocalization of C at m, and its inverse F -> T Pi(F is an element of F).
We construct a similar correspondence for n-tilting modules using compatible families of localizations; however, there is no explicit formula for the inverse. (C) 2014 Elsevier Inc. All rights reserved.