2014/06/02 by Ivan Panin, Panin, Ivan
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.1406.0241
arXiv admin note: substantial text overlap with arXiv:0905.1418
arxiv created 2014/06/02 · openalex publication_date 2014/06/02 · arxiv updated 2014/06/03 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28
In three preprints [Pan2],[Pan3] and the present one we prove Grothendieck-Serre's conjecture concerning principal G-bundles over regular semi-local domains R containing a finite field (here G is a reductive group scheme). The present preprint contains main geometric presentation theorems which are necessary for that. The preprint [Pan2] contains reduction of the Grothendieck-Serre's conjecture to the case of a simple simply-connected group scheme. The preprint [Pan3] contains a proof of Grothendieck-Serre's conjecture for regular semi-local domains R containing a finite field. One of the main result of the present preprint is Theorem 1.1. The Grothendieck--Serre conjecture for the case of regular semi-local domains containing an infinite field is proven in joint work due to R.Fedorov and I.Panin (see [FP]). Thus the conjecture holds for regular semi-local domains containing a field.