Around rationality of cycles
Open Mathematics (2013)
- Volume: 11, Issue: 6, page 1068-1077
- ISSN: 2391-5455
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topRaphaël Fino. "Around rationality of cycles." Open Mathematics 11.6 (2013): 1068-1077. <http://eudml.org/doc/268998>.
@article{RaphaëlFino2013,
abstract = {We prove certain results comparing rationality of algebraic cycles over the function field of a quadric and over the base field. These results have already been obtained by Alexander Vishik in the case of characteristic 0, which allowed him to work with algebraic cobordism theory. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2.},
author = {Raphaël Fino},
journal = {Open Mathematics},
keywords = {Chow groups; Quadrics; Steenrod operations; quadrics},
language = {eng},
number = {6},
pages = {1068-1077},
title = {Around rationality of cycles},
url = {http://eudml.org/doc/268998},
volume = {11},
year = {2013},
}
TY - JOUR
AU - Raphaël Fino
TI - Around rationality of cycles
JO - Open Mathematics
PY - 2013
VL - 11
IS - 6
SP - 1068
EP - 1077
AB - We prove certain results comparing rationality of algebraic cycles over the function field of a quadric and over the base field. These results have already been obtained by Alexander Vishik in the case of characteristic 0, which allowed him to work with algebraic cobordism theory. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2.
LA - eng
KW - Chow groups; Quadrics; Steenrod operations; quadrics
UR - http://eudml.org/doc/268998
ER -
References
top- [1] Brosnan P., Steenrod operations in Chow theory, Trans. Amer. Math. Soc., 2003, 355(5), 1869–1903 http://dx.doi.org/10.1090/S0002-9947-03-03224-0[Crossref] Zbl1045.55005
- [2] Elman R., Karpenko N., Merkurjev A., The Algebraic and Geometric Theory of Quadratic Forms, Amer. Math. Soc. Colloq. Publ., 56, American Mathematical Society, Providence, 2008 Zbl1165.11042
- [3] Fino R., Around rationality of integral cycles, J. Pure Appl. Algebra (in press), preprint available at http://www.math.uni-bielefeld.de/LAG/man/462.pdf
- [4] Karpenko N.A., Variations on a theme of rationality of cycles, Cent. Eur. J. Math., 2013, 11(6), 1056–1067 http://dx.doi.org/10.2478/s11533-013-0228-6[Crossref][WoS] Zbl1300.14008
- [5] Vishik A., Generic points of quadrics and Chow groups, Manuscripta Math., 2007, 122(3), 365–374 http://dx.doi.org/10.1007/s00229-007-0074-6[WoS][Crossref] Zbl1154.14003
- [6] Vishik A., Symmetric operations in algebraic cobordisms, Adv. Math., 2007, 213(2), 489–552 http://dx.doi.org/10.1016/j.aim.2006.12.012[Crossref]
- [7] Vishik A., Fields of u-invariant 2r + 1, In: Algebra, Arithmetic, and Geometry: in Honor of Yu.I. Manin, II, Progr. Math., 270, Birkhäuser, Boston, 2009, 661–685 http://dx.doi.org/10.1007/978-0-8176-4747-6_22[Crossref]
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