On composition of torsors
Résumé
Let K be a field, let X be a connected smooth K-scheme and let G, H be two smooth connected K-group schemes. Given Y → X a G-torsor and Z → Y an H-torsor, we study whether one can find an extension E of G by H so that the composite Z → X is an E-torsor. We give both positive and negative results, depending on the nature of the groups G and H.
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