On Brauer Groups of Double Covers of Ruled
نویسندگان
چکیده
— Let X be a smooth double cover of a geometrically ruled surface defined over a separably closed field of characteristic different from 2. The main result of this paper is a finite presentation of the 2-torsion in the Brauer group of X with generators given by central simple algebras over the function field of X and relations coming from the Néron-Severi group of X. The path to this result naturally involves a study of the 2-torsion Brauer classes of a smooth double cover of the projective line, yielding results of independent interest. Arithmetic applications are given for both curves and surfaces.
منابع مشابه
On Brauer Groups of Double Covers of Ruled Surfaces
Let X be a smooth double cover of a geometrically ruled surface defined over a separably closed field of characteristic different from 2. The main result of this paper is a finite presentation of the 2-torsion in the Brauer group of X with generators given by central simple algebras over the function field of X and relations coming from the NéronSeveri group of X. In particular, the result give...
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