Constant case of the Grothendieck-Serre conjecture in mixed characteristic

TL;DR

This paper proves the Grothendieck-Serre conjecture for reductive group schemes over mixed characteristic DVRs and regular local algebras, and extends a geometric presentation lemma to this setting.

Contribution

It establishes the conjecture in mixed characteristic for a broad class of algebraic structures and generalizes a key geometric lemma.

Findings

Grothendieck-Serre conjecture verified for reductive D-group schemes

Extension of Lindel-Ojanguren-Gabber's lemma to DVR context

Advancement in understanding algebraic groups over mixed characteristic rings

Abstract

Let D be a DVR of mixed characteristic. Let G be a reductive D-group scheme. Then the Grothendieck-Serre conjecture is true for the D-group scheme G and any geometrically regular local D-algebra R. Also we prove a version of Lindel-Ojanguren-Gabber's geometric presentation lemma in the DVR context.