On the Grothendieck-Serre conjecture on principal bundles in mixed characteristic

Abstract

Let R be a regular local ring. Let G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle over R is trivial if it is trivial over the quotient field of R. The conjecture is known when R contains a field. We prove the conjecture for a large class of regular local rings not containing fields in the case when G is split.

The final version to be published in Transactions of the AMS. Results about quadratic forms are strengthened. In the section on Bertini type theorems a correction in the case of a non-perfect residue field is made. Other minor corrections and improvements

References in corpus (2)

• Affine Grassmannians of group schemes and exotic principal bundles over A^1
• The Grothendieck-Serre Conjecture over Semilocal Dedekind Rings

Cited by in corpus (1)

• Purity and quasi-split torsors over Prüfer bases