Variations on a theme of rationality of cycles
Open Mathematics (2013)
- Volume: 11, Issue: 6, page 1056-1067
- ISSN: 2391-5455
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topNikita Karpenko. "Variations on a theme of rationality of cycles." Open Mathematics 11.6 (2013): 1056-1067. <http://eudml.org/doc/269452>.
@article{NikitaKarpenko2013,
abstract = {We prove certain weak versions of some celebrated results due to Alexander Vishik comparing rationality of algebraic cycles over the function field of a quadric and over the base field. The original proofs use Vishik’s symmetric operations in the algebraic cobordism theory and work only in characteristic 0. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2. Our weak versions are still sufficient for existing applications. In particular, Vishik’s construction of fields of u-invariant 2r + 1, for r ≥ 3, is extended to arbitrary characteristic ≠ 2.},
author = {Nikita Karpenko},
journal = {Open Mathematics},
keywords = {Chow groups; Quadrics; Steenrod operations; u-invariant; quadrics; -invariant},
language = {eng},
number = {6},
pages = {1056-1067},
title = {Variations on a theme of rationality of cycles},
url = {http://eudml.org/doc/269452},
volume = {11},
year = {2013},
}
TY - JOUR
AU - Nikita Karpenko
TI - Variations on a theme of rationality of cycles
JO - Open Mathematics
PY - 2013
VL - 11
IS - 6
SP - 1056
EP - 1067
AB - We prove certain weak versions of some celebrated results due to Alexander Vishik comparing rationality of algebraic cycles over the function field of a quadric and over the base field. The original proofs use Vishik’s symmetric operations in the algebraic cobordism theory and work only in characteristic 0. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2. Our weak versions are still sufficient for existing applications. In particular, Vishik’s construction of fields of u-invariant 2r + 1, for r ≥ 3, is extended to arbitrary characteristic ≠ 2.
LA - eng
KW - Chow groups; Quadrics; Steenrod operations; u-invariant; quadrics; -invariant
UR - http://eudml.org/doc/269452
ER -
References
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- [8] Vishik A., Symmetric operations in algebraic cobordism, Adv. Math., 2007, 213(2), 489–552 http://dx.doi.org/10.1016/j.aim.2006.12.012[WoS][Crossref] Zbl1129.14034
- [9] 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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