ON THE GROTHENDIECK-SERRE CONJECTURE CONCERNING PRINCIPAL G-BUNDLES OVER SEMILOCAL DEDEKIND DOMAINS

摘要

Let R be a semilocal Dedekind domain, and let K be the field of fractions of R. Let G be a reductive semisimple simply connected R-group scheme such that every semisimple normal R-subgroup scheme of G contains a split R-torustIt is proved that the kernel of the map H_(ét)~1(R,G) →H_(ét)~1(K,G) induced by the inclusion of R into K is trivial. This result partially extends the Nisnevich theorem. Bibliography: 18 titles.