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arXiv · 2604.07243

Sha-rigidity of adjoint Chevalley groups of types $A_1$, $A_2$, $B_2$, $G_2$ over commutative rings

Elena Bunina·Vazgen Kirakosyan·Rachel Treskunov
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Abstract

We prove that every locally inner (class-preserving) endomorphism of adjoint Chevalley groups and their elementary subgroups over commutative rings is inner for the root systems A1, A2, B2 (assuming 2 is invertible in the ring), and for G2 (assuming 2 and 3 are invertible). As a consequence, these groups are Sha-rigid. The proofs are direct and do not rely on classification of automorphisms or structural results about injective endomorphisms.

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Elena Bunina, Vazgen Kirakosyan, Rachel Treskunov. 2026-04-08. Sha-rigidity of adjoint Chevalley groups of types $A_1$, $A_2$, $B_2$, $G_2$ over commutative rings. https://doi.org/10.46298/jgcc.2026.18.2.17981

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