Vladimir Chernousov and Ivan Panin: Purity of $F_4$--torsors with trivial $g_3$ invariant

chernous@math.ualberta.ca, panin@pdmi.ras.ru

Submission: 2009, Aug 25

We prove that the functor of n-fold Pfister forms satisfies purity for regular local rings containing the field of rational numbers. As an application we show that purity holds for $F_4$-torsors with trivial $g_3$ invariant.

2000 Mathematics Subject Classification: 14L15, 20G10, 11E72

Keywords and Phrases: Linear algebraic group, exceptional groups, torsor, non-abelian cohomology, Pfister forms, purity conjecture

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