Sha-rigidity of Chevalley groups over local rings
Abstract
We prove that every locally inner endomorphism of a Chevalley group (or its elementary subgroup) over a local ring with an irreducible root system of rank >1 (with 1/2 for the systems A2, F4, Bl, Cl and with 1/3 for the system G2) is inner, so that all these groups are Sha-rigid.
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