Abstract
Let R be a semilocal integral Dedekind domain and K be its fraction field. Let μ : G → T be an R-group scheme morphism between reductive R-group schemes that is smooth as a scheme morphism. Assume that T is an R-torus. Then the map T(R)/μ(G(R)) → T(K)/μ(G(K)) is injective, and a certain purity theorem is true. These and other results are derived from an extended form of the Grothendieck–Serre conjecture proven in the present paper for rings R as above. Bibliography: 21 titles.
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