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arXiv · 2308.10076

Sha-rigidity of Chevalley groups over local rings

Elena Bunina·Boris Kunyavskii
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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 A_2, F_4, B_l, C_l and with 1/3 for the system G_2) is inner, so that all these groups are Sha-rigid.

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Elena Bunina, Boris Kunyavskii. 2023-08-19. Sha-rigidity of Chevalley groups over local rings. https://arxiv.org/abs/2308.10076

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