Independence of the total reflexivity conditions for modules
Abstract
Description
We show that the conditions defining total reflexivity for modules are independent. In particular, we construct a commutative Noetherian local ring $R$ and a reflexive $R$-module $M$ such that $\Ext^i_R(M,R)=0$ for all $i>0$, but $\Ext^i_R(M^*,R)\ne 0$ for all $i>0$.
In the previous version, Proposition 2.1 is incorrect, as stated. We added the assumption "Artinian" in the statement
In the previous version, Proposition 2.1 is incorrect, as stated. We added the assumption "Artinian" in the statement