A note on Gersten's conjecture for logarithmic Hodge-Witt sheaves
Let \(X\) be a smooth algebraic scheme over a perfect field \(k\) of characteristic \(p > 0\). Any time we are provided with purity theorems for logarithmic Hodge-Witt sheaves \(W_* \Omega^\bullet_{X, \log}\) the Cousin complex, canonically associated with these sheaves, yields a Gersten resolution of \(R^m \eta^* W_n \Omega^i_{X, \log}\) where \(\eta : X_{et} \to X_{Zar}\). In this paper a proof for the case of \(m = 1\) and \(i = \dim (X)\) is given, by showing local cohomological purity of \(W_n \Omega^i_{X, \log}\). Finally, some standard applications to the study of the \(p\)-primary part of \(K\)-cohomology are explained, in particular: finiteness of \(p\)-torsion of zero-cycles.
finiteness of \(p\)-torsion of zero-cycles
purity theorems for logarithmic Hodge-Witt sheaves
scientific article; zbMATH DE number 790463
scientific article