The Brauer Group of K3 Covers

El grupo de Brauer de K3 cubrimientos

HERMES MARTÍNEZ1

1Universidad Sergio Arboleda, Bogotá, Colombia. Email: hermes.martinez@usa.edu.co


Abstract

In this paper we study the injectivity of the induced morphism on the Brauer groups π*: Br'(Y) → Br'(X) given by the K3 cover π:X → Y of the Enriques surface Y.

Key words: Brauer group, K3 surface, Hochschild--Serre spectral sequence.


2000 Mathematics Subject Classification: 14J28, 16K50, 20J062.

Resumen

En este artículo estudiamos la inyectividad del morfismo inducido sobre los grupos de Brauer π*: Br(Y) → Br(X) dado por el K3 cubrimiento π:X → Y de la superficie de Enriques Y.

Palabras clave: Grupo de Brauer, superficie K3, sucesión espectral de Hochschild--Serre.


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References

[1] W. Barth, K. Hulek, C. Peters, and A. V. d. Ven, Compact Complex Surfaces, Vol. 4 of Modern Surveys in Mathematics, 2nd edn, Springer Verlag, Berlin, Germany, 2004.

[2] A. Beauville, 'On the Brauer Group of Enriques Surfaces', Math. Research Letters 16, (2009), 927-934.

[3] D. Harari and A. Skorobogatov, 'Non-abelian Descent and the Arithmetic of Enriques Surfaces', Int. Math. Res. Not., 52 (2005), 3203-3228.

[4] K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Vol. 84 of Graduate Texts in Mathematics, Springer-Verlag, New York, USA, 1990.

[5] J. S. Milne, Lectures on Etale Cohomology (v2.20), (2012). Available at http://www.jmilne.org/math/

[6] D. Morrison, 'On K3 Surfaces with large Picard Number', Invent. Math. 75, 1 (1984), 105-121.

[7] D. Naie, 'Special Rank Two Vector Bundles over Enriques Surfaces', Mathematische Annalen 300, 1 (1994), 297-316.

[8] V. V. Nikulin, 'Factor Groups of Groups of Automorphisms of Hyperbolic Forms with respect to Subgroups Generated by 2-reflections', J. Soviet Math. 22, (1983), 1401-1476. English Translation

[9] H. Ohashi, 'On the Number of Enriques Quotients of a K3 Surface', Publ. Res. Inst. Math. Sci. 43, 1 (2007), 181-200.

[10] R. L. E. Schwarzenberger, 'Vector Bundles on Algebraic Surfaces', Proc. London Math. Soc. 3, 11 (1961), 601-622.

[11] C. Weibel, An Introduction to Homological Algebra, Cambridge University Press, Cambridge University Press, Cambridge, UK, 1994.


(Recibido en mayo de 2012. Aceptado en octubre de 2012)

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv46n2a05,
    AUTHOR  = {Martínez, Hermes},
    TITLE   = {{The Brauer Group of K3 Covers}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2012},
    volume  = {46},
    number  = {2},
    pages   = {185--204}
}