Grothendieck-Serre conjecture for adjoint groups of types E₆ and E₇ and for certain classical groups

2009/05/09 by Ivan Panin, Panin, I., V. A. Petrov +3
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.0905.1427

openalex publication_date 2009/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Assume that R is a semi-local regular ring containing an infinite perfect field, or that R is a semi-local ring of several points on a smooth scheme over an infinite field. Let K be the field of fractions of R. Let H be a strongly inner adjoint simple algebraic group of type E₆ or E₇ over R, or any twisted form of one of the split groups of classical type O⁺_n,R, n>=4; PGO_n,R, n>=4; PSp_2n,R, n>=2; PGL_n,R, n>=2. We prove that the kernel of the map H¹_et(R,H)-> H¹_et(K,H) induced by the inclusion of R into K is trivial. This continues the recent series of papers by the authors and N. Vavilov on the Grothendieck--Serre conjecture.

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