Steinberg pro-groups for GL, odd unitary, and Chevalley groups satisfy the Zariski cosheaf property as crossed pro-modules, with an analogue of commutator formulas and an action of base groups over localized rings.
A presentation of relative unitary Steinberg groups
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abstract
We find an explicit presentation of relative odd unitary Steinberg groups constructed by odd form rings and of relative doubly laced Steinberg groups over commutative rings, i.e. the Steinberg groups associated with the Chevalley group schemes of the types $\mathsf B_\ell$, $\mathsf C_\ell$, $\mathsf F_4$ for $\ell \geq 3$. For simply laced root systems such result is already known.
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math.GR 1years
2023 1verdicts
UNVERDICTED 1representative citing papers
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Cosheaves of Steinberg pro-groups
Steinberg pro-groups for GL, odd unitary, and Chevalley groups satisfy the Zariski cosheaf property as crossed pro-modules, with an analogue of commutator formulas and an action of base groups over localized rings.