Noetherian Algebras of Finite Self-Injective Dimension

Abstract

Let R be a commutative noetherian ring and A a noetherian R-algebra. Take a minimal injective resolution R → I ^• and set . We deal with the case where V ^• is a dualizing complex for A. We show that A itself is a dualizing complex for A if and only if V ^• is isomorphic to a tilting complex in 𝒟(\textMod-A) and that if A is a dualizing complex for A, then induces a self-equivalence of 𝒟 ^b(\textmod-A).

Key Words:

• Derived equivalence
• Dualizing complex
• Noetherian algebra
• Tilting complex

2000 Mathematics Subject Classification:

• Primary 18E30, 16E10
• Secondary 16G30

ACKNOWLEDGMENT

The author would like to thank M. Hoshino for his helpful advice.

Notes

Communicated by D. Zacharia