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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.07243 |
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| _version_ | 1866918471560855552 |
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| author | Bunina, Elena Kirakosyan, Vazgen Treskunov, Rachel |
| author_facet | Bunina, Elena Kirakosyan, Vazgen Treskunov, Rachel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07243 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sha-rigidity of adjoint Chevalley groups of types $A_1$, $A_2$, $B_2$, $G_2$ over commutative rings Bunina, Elena Kirakosyan, Vazgen Treskunov, Rachel Group Theory Algebraic Geometry 20G35, 20F16, 20F10 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. |
| title | Sha-rigidity of adjoint Chevalley groups of types $A_1$, $A_2$, $B_2$, $G_2$ over commutative rings |
| topic | Group Theory Algebraic Geometry 20G35, 20F16, 20F10 |
| url | https://arxiv.org/abs/2604.07243 |