The Gersten conjecture for Witt groups in the equicharacteristic case
For an \(n\)-dimensional regular local ring \(R\) write \(X\) for the spectrum of \(R\) and \(X^{(p)}\) for the primes of height \(p\). The Gersten-Witt complex connects the Witt groups of the residue fields at points in \(X^{(i)}\) and \(X^{(i+1)}\). The augmented Gersten-Witt complex, \(\text{GWC}_a(R)\), is the Gersten-Witt complex augmented by the natural map \(W(R) \rightarrow W(K)\), where \(K\) is the field of fractions of \(R\). The main result of the paper asserts that \(\text{GWC}_a(R)\) is exact for any regular local ring containing some field (equicharacteristic regular local ring). The bulk of the paper consists of explanations how the results in the existing literature are going to be used, and then the proof of the main result is given without much effort on less than one printed page.
scientific article; zbMATH DE number 1862887