The maximal unipotent finite quotient, unusual torsion in Fano
threefolds, and exceptional Enriques surfaces
Authors: Andrea Fanelli ; Stefan Schröer
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Andrea Fanelli;Stefan Schröer
We introduce and study the maximal unipotent finite quotient for algebraic
group schemes in positive characteristics. Applied to Picard schemes, this
quotient encodes unusual torsion. We construct integral Fano threefolds where
such unusual torsion actually appears. The existence of such threefolds is
surprising, because the torsion vanishes for del Pezzo surfaces. Our
construction relies on the theory of exceptional Enriques surfaces, as
developed by Ekedahl and Shepherd-Barron.