The constant case of the Grothendieck-Serre conjecture is proved for reductive group schemes over any geometrically regular local algebra over a mixed-characteristic DVR.
Weak elementary fibrations
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abstract
We introduce a notion of a weak elementary fibration and prove that it does exist in certain interesting cases. Our notion is a modification of the M. Artin's notion of an elementary fibration.
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Constant case of the Grothendieck-Serre conjecture in mixed characteristic
The constant case of the Grothendieck-Serre conjecture is proved for reductive group schemes over any geometrically regular local algebra over a mixed-characteristic DVR.