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.
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Explicit presentations are given for relative Steinberg groups of types Bℓ, Cℓ, F4 (ℓ≥3) and odd unitary Steinberg groups over the specified rings.
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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.
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A presentation of relative unitary Steinberg groups
Explicit presentations are given for relative Steinberg groups of types Bℓ, Cℓ, F4 (ℓ≥3) and odd unitary Steinberg groups over the specified rings.