On the Brauer group of an algebraic variety over a finite field

T. V. Zasorina

Vladimir State University

Abstract: For an arithmetic model $X\to C$ of a smooth regular projective variety $V$ over a global field $k$ of positive characteristic, we prove the finiteness of the $l$-primary component of the group $\operatorname{Br}'(X)$ under the conditions that $l$ does not divide the order of the torsion group $\bigl[\operatorname{NS}(V)\bigr]_{\text{tors}}$ and the Tate conjecture on divisorial cohomology classes is true for $V$.

UDC: 512.6

MSC: 11G35, 11R37, 11R42, 11S40, 11S80, 14C22, 14F22, 14J28, 14F22

Received: 16.03.2004

DOI: 10.4213/im635

 English version: Izvestiya: Mathematics, 2005, 69:2, 331–343

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