A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields

TL;DR

This paper proves that principal G-bundles over regular local rings containing infinite fields are trivial if they are trivial over the fraction field, confirming a significant case of the Grothendieck-Serre conjecture.

Contribution

It establishes the Grothendieck-Serre conjecture for principal bundles over regular local rings with infinite fields, a key open problem in algebraic geometry.

Findings

Principal G-bundles over R are trivial if trivial over the fraction field.

The result confirms the conjecture for a broad class of rings and group schemes.

Advances understanding of the structure of principal bundles in algebraic geometry.

Abstract

Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R.