Alexandra Zvonareva

Silting Theory in triangulated categories with coproducts (jt. with Pedro Nicolas and Manuel Saorin)

Abstract:

We introduce the notions of noncompact (partial) silting and (partial) tilting sets and objects in any triangulated category D with arbitrary (set-indexed) coproducts. We show that the equivalence classes of partial silting sets are in bijection with t-structures generated by their co-heart whose heart has a generator. We describe the objects in the aisle of the t-structure associated to a partial silting set T as the Milnor colimits of sequences of morphisms with successive cones in Sum(T)[n]. We use this fact to develop a theory of tilting objects in very general AB3 abelian categories and show the validity of several well-known results of tilting and cotilting theory of modules.