Witt rings of fields of quotients of two-dimensional regular local rings
Let \(R\) be a regular local ring of Krull dimension two, which contains \({1\over 2}\). Let \(\overline {R}\) be its field of quotients. The aim of this paper is to show that the following sequence of Witt groups is exact: \[ 0\to W(R)@>j^*>>W(\overline{R}) @>\oplus\partial_ p>> \bigoplus_{p\in P} W(\overline {R/p}) \to W(R/m)\to 0, \] where \(j^*\) is induced by the canonical imbedding \(j: R\to\overline {R}\) and \(P\) is the set of all prime ideals of the ring \(R\) of height 1.
regular local ring of Krull dimension two
scientific article; zbMATH DE number 126411
scientific article