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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.46 no.2 Bogotá July/Dec. 2012

 

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.


Texto completo disponible en PDF


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,         [ Links ] 2004.

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

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

[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,         [ Links ] 1990.

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

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

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

[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         [ Links ]

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

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

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