Dans cette Note, on établit une formule générale pour la cohomologie non ramifiée des corps dʼinvariants linéaires sous des groupes finis. Des telles formules sont connues en degré 2 et 3.
In this Note, we establish a general formula for the unramified cohomology of fields of linear invariants by finite groups. Such formulas are known in degree 2 and 3.
Accepté le :
Publié le :
Thi Kim Ngan Nguyen 1
@article{CRMATH_2011__349_5-6_233_0, author = {Thi Kim Ngan Nguyen}, title = {Classes non ramifi\'ees sur un espace classifiant}, journal = {Comptes Rendus. Math\'ematique}, pages = {233--237}, publisher = {Elsevier}, volume = {349}, number = {5-6}, year = {2011}, doi = {10.1016/j.crma.2011.02.012}, language = {fr}, }
Thi Kim Ngan Nguyen. Classes non ramifiées sur un espace classifiant. Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 233-237. doi : 10.1016/j.crma.2011.02.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.02.012/
[1] Variétés unirationnelles non rationnelles : au delà de lʼexemple dʼArtin et Mumford, Invent. Math., Volume 97 (1989), pp. 141-158
[2] The rationality problem for fields of invariants under linear algebraic groups (with special regards to the Brauer group), Mumbai, 2004 (V. Mehta, ed.), Narosa Publishing House, TIFR Mumbai (2007), pp. 113-186
[3] Bivariant cycle cohomology, Cycles, Transfers and Motivic Cohomology Theories, Annals of Mathematics Studies, vol. 143, Princeton University Press, Princeton, NJ, 2000, pp. 188-238
[4] Etale Cohomology, Princeton University Press, 1980
[5] Lecture Notes on Motivic Cohomology, Clay Mathematics Monographs, vol. 2, Amer. Math. Soc., 2006
[6] T.-K.-Ngan Nguyen, Modules de cycles et classes non ramifiées sur un espace classifiant, Thèse de lʼUniversité Paris VII, 2010, http://www.math.jussieu.fr/~ngannguyen/These-NguyenTKN1.pdf.
[7] Unramified cohomology of degree 3 and Noetherʼs problem, Invent. Math., Volume 171 (2008), pp. 191-225
[8] Chow groups with coefficients, Doc. Math., Volume 1 (1996), pp. 319-393
[9] The Chow ring of a classifying space (W. Raskind; C. Weibel, eds.), Algebraic K-Theory, Proceedings of Symposia in Pure Mathematics, vol. 67, American Mathematical Society, 1999, pp. 249-281
[10] Cohomological theory of presheaves with transfers, Cycles, Transfers and Motivic Cohomology Theories, Annals of Mathematics Studies, vol. 143, Princeton University Press, 2000, pp. 87-137
Cité par Sources :
Commentaires - Politique