2014/06/02 by Ivan Panin, Panin, Ivan
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG
paper · pdf · doi:10.48550/arxiv.1406.1129
arXiv admin note: substantial text overlap with arXiv:0905.1423
arxiv created 2014/06/02 · openalex publication_date 2014/06/02 · arxiv updated 2014/06/05 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In three preprints [Pan1], [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 preprint [Pan1] contains main geometric presentation theorems which are necessary for that. The present preprint contains reduction of the Grothendieck--Serre's conjecture to the case of semi-simple simply-connected group schemes (see Theorem 1.0.1). The preprint [Pan3] contains a proof of that conjecture for regular semi-local domains R containing a finite field. 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. The reduction is based on two purity results (Theorem 1.0.2 and Theorem 10.0.29).