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.
Moving lemmas in mixed characteristic and applications
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
fields
math.AG 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
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.