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Moving lemmas in mixed characteristic and applications

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arxiv 2202.00896 v1 pith:SPFJKK2K submitted 2022-02-02 math.KT

Ivan Panin This is my paper · ORCID
classification math.KT
keywords resultcharacteristicconjecturegeometricmixedprovedquadraticspaces
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The present paper contains new geometric theorems in mixed characteristic case. We derive a bunch of cohomological consequences using these geometric theorems. Among them an isotropy result for quadratic spaces, a purity result for quadratic spaces, a result on the Grothendieck--Serre conjecture for the special linear group of an Azumaya algebra. The Gersten conjecture for the functor K2 is proved. Bloch-Ogus type result is obtained as well. Suslin's exact sequence is derived and its application to a finiteness result is given. A version of the Roitman theorem is proved.

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  1. Constant case of the Grothendieck-Serre conjecture in mixed characteristic

    math.AG 2024-12 conditional novelty 8.0 of 10

    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.

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