Abstract
We show the Gersten's conjecture for \'etale cohomology over two dimensional henselian regular local rings without assuming equi-characteristic. As application, we obtain the local-global principle for Galois cohomology over mixed characteristic two-dimensional henselian local rings.
Highlights
Let R be an equi-characteristic regular local ring, k(R) the field of fractions of R, l a positive integer which is invertible in R and μl the étale sheaf of l -th roots of unity
The following question was raised by Colliot-Thélène ([3]): Let n ≥ 1 be an integer and l a positive integer which is invertible in R
Let R be a regular local ring and l a positive integer which is invertible in R
Summary
A note on Gersten’s conjecture for étale cohomology over two-dimensional henselian regular local rings Volume 358, issue 1 (2020), p. Mathématique sont membres du Centre Mersenne pour l’édition scientifique ouverte www.centre-mersenne.org
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