GROTHENDIECK—SERRE CONJECTURE FOR GROUPS OF TYPE F4 WITH TRIVIAL f3 INVARIANT

Assume that R is a semi-local regular ring containing an infinite perfect field. Let K be the field of fractions of R. Let H be a simple algebraic group of type F4 over R such that HK is the automorphism group of a 27-dimensional Jordan algebra which is a first Tits construction. If charK 6= 2 this means precisely that the f3 invariant of HK is trivial. We prove that the kernel of the map H ét (R, H) → H ét (K, H) induced by the inclusion of R into K is trivial. This result is a particular case of the Grothendieck—Serre conjecture on rationally trivial torsors. It continues the recent series of papers [PaSV], [Pa], [PaPS] and complements the result of Chernousov [Ch] on the Grothendieck—Serre conjecture for groups of type F4 with trivial g3 invariant.