Variations on a Theme of Groups Splitting by a Quadratic Extension and Grothendieck-Serre Conjecture for Group Schemes
نویسندگان
چکیده
We study structure properties of reductive group schemes defined over a local ring and splitting over its étale quadratic extension. As an application we prove Serre–Grothendieck conjecture on rationally trivial torsors over a local regular ring containing a field of characteristic 0 for group schemes of type F4 with trivial g3 invariant. 2010 Mathematics Subject Classification: 20G07, 20G10, 20G15, 20G41
منابع مشابه
VARIATIONS ON A THEME OF GROUPS SPLITTING BY A QUADRATIC EXTENSION AND GROTHENDIECK-SERRE CONJECTURE FOR GROUP SCHEMES F4 WITH TRIVIAL g3 INVARIANT
We study structure properties of reductive group schemes defined over a local ring and splitting over its étale quadratic extension. As an application we prove Serre–Grothendieck conjecture on rationally trivial torsors over a local regular ring containing a field of characteristic 0 for group schemes of type F4 with trivial g3 invariant.
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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 ...
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