On Partial Tilting Complexes

Abstract

Let R be a commutative noetherian ring and A a noetherian R-algebra. Let P ^• ∈ 𝒦^b(𝒫 _A ) with Hom_𝒦(Mod-A)(P ^•, P ^•[i]) = 0 for i > 0. We will provide a sufficient condition for P ^• to be a direct summand of a silting complex. Also, in case Hom_𝒦(Mod-A)(P ^•, P ^•[i]) = 0 for i ≠ 0, we will provide a sufficient condition for P ^• to be a direct summand of a tilting complex.

Key Words:

• Partial tilting complex
• Silting complex
• Tilting complex
• Tilting module

2000 Mathematics Subject Classification:

• Primary 16E05, 16E10
• Secondary 16E30

Notes

Communicated by D. Zacharia.