Over a normal base scheme, we prove the generalized Theorem of the Cube for 1-motives and that a torsion class of the group He´t2(M,Gm,M) of a 1-motive M, whose pull-back via the unit section ϵ:S→M is zero, comes from an Azumaya algebra. In particular, we deduce that over an algebraically closed field of characteristic zero, all classes of He´t2(M,Gm,M) come from Azumaya algebras.
Brauer groups of 1-motives
Bertolin C.
;
2021
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 He´t2(M,Gm,M) of a 1-motive M, whose pull-back via the unit section ϵ:S→M is zero, comes from an Azumaya algebra. In particular, we deduce that over an algebraically closed field of characteristic zero, all classes of He´t2(M,Gm,M) come from Azumaya algebras.File in questo prodotto:
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