Weak purity for Gorenstein rings (Q1895630)

One studies module finite ring extensions \(B \hookrightarrow A\) of normal rings. The main result deals with \(B\) Gorenstein of dimension \(\geq 5\) and asserts that the condition \((R_k)\) for \(B\) implies \((S_{k - 1})\) for \(A\), when \(k \geq 4\). The proof uses maximal Cohen-Macaulay modules, so the result stated above is shown in the equicharacteristic case, using the existence theorem of such modules due to M. Hochster. The mixed characteristic case is treated separately, under supplementary conditions. Applications are given.