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Introduction to the Ekedahl Invariants

Ivan Martino

Abstract


In 2009, T. Ekedahl introduced certain cohomological invariants for finite groups. In this work we present these invariants and we give an equivalent definition that does not involve the notion of algebraic stacks. Moreover we show certain properties for the class of the classifying stack of a finite group in the Kontsevich value ring.

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References


Artin, M. and Mumford, D., Some elementary examples of unirational varieties which are not rational, Proc. London Math. Soc. (3) 25 (1972), 75–95. https://doi.org/10.1112/plms/s3-25.1.75

Bittner, F., The universal Euler characteristic for varieties of characteristic zero, Compos. Math. 140 (2004), no. 4, 1011–1032. https://doi.org/10.1112/S0010437X03000617

Bogomolov, F. A., The Brauer group of quotient spaces of linear representations, Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987), no. 3, 485–516.

Ekedahl, T., A geometric invariant of a finite group, preprint arXiv:0903.3148v1 [math.AG], 2009.

Ekedahl, T., The Grothendieck group of algebraic stacks, preprint arXiv:0903.3143v2 [math.AG], 2009.

Fulton, W., Intersection theory, second ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 2, Springer-Verlag, Berlin, 1998. https://doi.org/10.1007/978-1-4612-1700-8

Hatcher, A., Algebraic topology, Cambridge University Press, Cambridge, 2002.

Hoshi, A., Kang, M.-C., and Kunyavskii, B. E., Noether's problem and unramified Brauer groups, Asian J. Math. 17 (2013), no. 4, 689–713. https://doi.org/10.4310/AJM.2013.v17.n4.a8

Kang, M.-c., Retract rationality and Noether's problem, Int. Math. Res. Not. IMRN (2009), no. 15, 2760–2788. https://doi.org/10.1093/imrn/rnp032

Manin, J. I., Correspondences, motifs and monoidal transformations, Mat. Sb. (N.S.) 77 (119) (1968), 475–507.

Martino, I., The Ekedahl invariants for finite groups, J. Pure Appl. Algebra 220 (2016), no. 4, 1294–1309. https://doi.org/10.1016/j.jpaa.2015.08.019

Noether, E., Gleichungen mit vorgeschriebener Gruppe, Math. Ann. 78 (1917), no. 1, 221–229. https://doi.org/10.1007/BF01457099

Saltman, D. J., Noether's problem over an algebraically closed field, Invent. Math. 77 (1984), no. 1, 71–84. https://doi.org/10.1007/BF01389135

Serre, J.-P., On the fundamental group of a unirational variety, J. London Math. Soc. 34 (1959), 481–484. https://doi.org/10.1112/jlms/s1-34.4.481

Swan, R. G., Invariant rational functions and a problem of Steenrod, Invent. Math. 7 (1969), 148–158. https://doi.org/10.1007/BF01389798




DOI: http://dx.doi.org/10.7146/math.scand.a-25693

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