Abstract
Let K be the field of fractions of a henselian valuation ring A. Assume that the completion b K is a separable extension of K. Let Y be a K-variety, let G be an algebraic group over K, and let f : X! Y be a G-torsor over Y . We consider the induced map X(K)! Y (K), which is continuous for the topologies deduced from the valuation. If I denotes the image of this map, we prove that I is locally closed in Y (K); moreover, the induced surjection X(K)! I is a principal bundle with group G(K) (also topologized by the valuation).
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