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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 $V$.
Received: 16.03.2004
Citation:
T. V. Zasorina, “On the Brauer group of an algebraic variety over a finite field”, Izv. RAN. Ser. Mat., 69:2 (2005), 111–124; Izv. Math., 69:2 (2005), 331–343
Linking options:
https://www.mathnet.ru/eng/im635https://doi.org/10.1070/IM2005v069n02ABEH000531 https://www.mathnet.ru/eng/im/v69/i2/p111
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Abstract page: | 460 | Russian version PDF: | 201 | English version PDF: | 15 | References: | 72 | First page: | 1 |
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