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A Note on the Height of the Formal Brauer Group of a $K3$ Surface

Published online by Cambridge University Press:  20 November 2018

Yasuhiro Goto
Yasuhiro Goto*
Affiliation:
Department of Mathematics Hokkaido University of Education 1-2 Hachiman-cho Hakodate 040-8567 Japan, e-mail: [email protected]
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Abstract

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Using weighted Delsarte surfaces, we give examples of $K3$ surfaces in positive characteristic whose formal Brauer groups have height equal to 5, 8 or 9. These are among the four values of the height left open in the article of Yui [11].

Keywords

14L0514J28formal Brauer groupsK3 surfaces in positive characteristicweighted Delsarte surfaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 1 , 01 March 2004 , pp. 22 - 29
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Artin, M., Supersingular K3 surfaces. Ann. Sci. École Norm. Sup. (4) 7 (1974), 543–568.Google Scholar
[2] Artin, M. and Mazur, B., Formal groups arising from algebraic varieties. Ann. Sci. É cole Norm. Sup. (4) 10 (1977), 87–132.Google Scholar
[3] Delsarte, J., Nombres de solutions des équations polynomiales sur un corps fini. Séminaire Bourbaki 39 (1951), 1–9.Google Scholar
[4] Dimca, A., Singularities and coverings of weighted complete intersections. J. Reine Angew.Math. 366 (1986), 184–193.Google Scholar
[5] Dolgachev, I., Weighted projective varieties. In: Lecture Notes in Math. 956, Springer, 1982, 34–71.Google Scholar
[6] Goto, Y., The Artin invariant of supersingular weighted Delsarte K3 surfaces. J. Math. Kyoto Univ. 36 (1996), 359–363.Google Scholar
[7] Shioda, T., An explicit algorithm for computing the Picard number of certain algebraic surfaces. Amer. J. Math. 108 (1986), 415–432.Google Scholar
[8] Shioda, T., Supersingular K3 surfaces with big Artin invariant. J. Reine Angew.Math. 381 (1987), 205–210.Google Scholar
[9] Shioda, T. and Katsura, T., On Fermat varieties. T.ohoku Math, J.. 31 (1979), 97–115.Google Scholar
[10] Suwa, N. and Yui, N., Arithmetic of Certain Algebraic Surfaces over Finite Fields. Lecture Notes in Math. 1383, Springer-Verlag, 1989, 186–256.Google Scholar
[11] Yui, N., Formal Brauer groups arising from certain weighted K3 surfaces. J. Pure Appl. Algebra 142 (1999), 271–296.Google Scholar