Brauer groups of 1-motives
Abstract
Over a normal base scheme, we prove the generalized Theorem of the Cube for 1-motives and that a torsion class of the group H2\'et(M,Gm)$ of a 1-motive M, whose pull-back via the unit section is zero, comes from an Azumaya algebra. In particular, we deduce that over an algebraically closed field of characteristic zero, all classes of H2\'et(M,Gm) come from Azumaya algebras.
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