Around rationality of cycles

• Autorzy: Raphaël Fino
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Chow groups; Quadrics; Steenrod operations

Kategorie tematyczne

• 11E04: Quadratic forms over general fields
• 14C25: Algebraic cycles

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 6
• Strony: 1068-1077

Daty

wydano

2013-06-01

online

2013-03-28

Twórcy

autor

Raphaël Fino

• Institut de Mathématiques de Jussieu, UPMC Sorbonne Universités, 4 Place Jussieu, Paris, 75020, France

Bibliografia

• [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]
• [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
• [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]
• [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]
• [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]

Identyfikatory

DOI

10.2478/s11533-013-0218-8