Incompressibility of Products of Pseudo-homogeneous Varieties
Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 824-833

Voir la notice de l'article provenant de la source Cambridge University Press

We show that the conjectural criterion of $p$ -incompressibility for products of projective homogeneous varieties in terms of the factors, previously known in a few special cases only, holds in general. Actually, the proof goes through for a wider class of varieties, including the norm varieties associated with symbols in Galois cohomology of arbitrary degree.
DOI : 10.4153/CMB-2016-024-4
Mots-clés : 20G15, 14C25, algebraic groups, projective homogeneous varieties, Chow groups and motives, canonical dimension and incompressibility
Karpenko, Nikita A. Incompressibility of Products of Pseudo-homogeneous Varieties. Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 824-833. doi: 10.4153/CMB-2016-024-4
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[1] [1] Berhuy, G. and Reichstein, Z., On the notion of canonical dimension for algebraic groups. Adv. Math. 198(2005), no. 1, 128–171. http://dx.doi.Org/10.1016/j.aim.2004.12.004 Google Scholar

[2] [2] Biswas, I., Dhillon, A., and Hoffmann, N., On the essential dimension of coherent sheaves. arxiv:1306.6432 Google Scholar

[3] [3] Elman, R., Karpenko, N., and Merkurjev, A., The algebraic and geometric theory of quadratic forms. American Mathematical Society Colloquium Publications 56, American Mathematical Society, Providence, RI, 2008. Google Scholar

[4] [4] Fulton, W., Intersection theory. Second ed. Ergebnisse der Mathematik und ihrer Grenzgebiete 2, Springer-Verlag, Berlin, 1998. Google Scholar

[5] [5] Karpenko, N. A., Incompressibility of products by Grassmannians ofisotropic subspaces. http://www.ualberta.ca/∼karpenko/publ/pbg-r.pdf Google Scholar

[6] [6] Karpenko, N. A., Canonical dimension. In: Proceedings of the International Congress of Mathematicians. II, New Delhi, Hindustan Book Agency, 2010. pp. 146–161. Google Scholar

[7] [7] Karpenko, N. A., Sufficiently generic orthogonal Grassmannians. J. Algebra 372(2012), 365–375. http://dx.doi.Org/10.1016/j.jalgebra.2012.09.021 Google Scholar

[8] [8] Karpenko, N. A., Upper motives of algebraic groups and incompressibility of Severi-Brauer varieties. J. Reine Angew. Math. 677(2013), 179–198. Google Scholar

[9] [9] Karpenko, N. A., Incompressibility of products of Weil transfers of generalized Severi-Brauer varieties. Math. Z. (2014), 1–11. http://dx.doi.Org/10.1017/S1474748011000090 Google Scholar

[10] [10] Karpenko, N. A. and Merkurjev, A. S., Canonical p-dimension of algebraic groups. Adv. Math. 205(2006), no. 2, 410–433. http://dx.doi.Org/10.1016/j.aim.2005.07.013 Google Scholar

[11] [11] Karpenko, N. A. and Merkurjev, A. S., Essential dimension of finite p-groups. Invent. Math. 172(2008), no. 3, 491–508. http://dx.doi.Org/10.1007/s00222-007-0106-6 Google Scholar

[12] [12] Karpenko, N. A. and Merkurjev, A. S., On standard norm varieties. Ann. Sci. Ec. Norm. Super. (4) 46(2013), no. 1,175-214. Google Scholar

[13] [13] Karpenko, N. A. and Merkurjev, A. S., Motivic decomposition of compactifications of certain group varieties. J. Reine Angew. Math., to appear. http://dx.doi.Org/10.1515/crelle-2O16-0015 Google Scholar

[14] [14] Karpenko, N. A. and Reichstein, Z., A numerical invariant for linear representations of finite groups. Comment. Math. Helv. 90(2015), no. 3, 667–701. With an appendix by Julia Pevtsova and Z. Reichstein. http://dx.doi.Org/10.41 71/CMH/367 Google Scholar

[15] [15] Lotscher, R., MacDonald, M., Meyer, A., and Reichstein, Z., Essential dimension of algebraic tori. J. Reine Angew. Math. 677(2013), 1–13. http://dx.doi.Org/10.1515/crelle.2O12.010 Google Scholar

[16] [16] Lotscher, R., MacDonald, M., Meyer, A., and Reichstein, Z., Essential p-dimension of algebraic groups whose connected component is a torus. Algebra Number Theory 7(2013), no. 8, 1817–1840. http://dx.doi.Org/10.2140/ant.2013.7.1817 Google Scholar

[17] [17] Merkurjev, A. S., Essential dimension. In: Quadratic Forms: Algebra, Arithmetic, and Geometry. Contemp. Math. 493, American Mathematical Society, Providence, RI, 2009, pp. 299–326. Google Scholar

[18] [18] Merkurjev, A. S., Essential dimension: a survey. Transform. Groups 18(2013), no. 2, 415–481. http://dx.doi.Org/10.1007/s00031-013-92 6-y Google Scholar

[19] [19] Vishik, A. and Zainoulline, K., Motivic splitting lemma. Doc. Math. 13(2008), 81–96. Google Scholar

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