Uniform annihilators of local cohomology

In this paper, we study the properties of noetherian rings containing uniform local cohomological annihilators. It turns out that all such rings should be universally catenary and locally equidimensional. We will prove a necessary and sufficient condition for such rings, which enables us to show that if a locally equidimensional ring R is the image of a Cohen–Macaulay ring, then R has a uniform local cohomological annihilator. Moreover, we will give a positive answer to a conjecture of Huneke [C. Huneke, Uniform bounds in noetherian rings, Invent. Math. 107 (1992) 203–223, Conjecture 2.13] about excellent rings with dimension no more than 5.