Transcendence degree of zero-cycles and the structure of Chow motives

• Autorzy: Sergey Gorchinskiy , Vladimir Guletskiĭ
• Języki publikacji: EN

Abstrakty

EN

In the paper we introduce a transcendence degree of a zero-cycle on a smooth projective variety X and relate it to the structure of the motive of X. In particular, we show that in order to prove Bloch’s conjecture for a smooth projective complex surface X of general type with p g = 0 it suffices to prove that one single point of a transcendence degree 2 in X(ℂ), over the minimal subfield of definition k ⊂ ℂ of X, is rationally equivalent to another single point of a transcendence degree zero over k. This can be of particular interest in the context of Bloch’s conjecture for those surfaces which admit a concrete presentation, such as Mumford’s fake surface, see [Mumford D., An algebraic surface with K ample, (K 2) = 9, p g = q = 0, Amer. J. Math., 1979, 101(1), 233–244].

Słowa kluczowe

EN

Algebraic cycles; Rational equivalence; Motives; Balanced correspondence; Generic cycle; Minimal field of definition; Transcendence degree; Bloch’s conjecture; Rational curve

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 559-568

Daty

wydano

2012-04-01

online

2012-01-18

Twórcy

autor

Sergey Gorchinskiy

• Steklov Mathematical Institute,

autor

Vladimir Guletskiĭ

• University of Liverpool, Mathematics & Oceanography Building,

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0130-z