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A CONSTRUCTION OF SURFACES WITH LARGE HIGHER CHOW GROUPS

  • TOMOHIDE TERASOMA (a1)
Abstract

In this paper, we construct surfaces in $\mathbf{P}^{3}$ with large higher Chow groups defined over a Laurent power series field. Explicit elements in higher Chow group are constructed using configurations of lines contained in the surfaces. To prove the independentness, we compute the extension class in the Galois cohomologies by comparing them with the classical monodromies. It is reduced to the computation of linear algebra using monodromy weight spectral sequences.

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[B] Bloch, S., Algebraic cycles and higher K -theory , Adv. Math. 61(3) (1986), 267304.
[CMS] Collino, A., Müller-Stach, S. and Saito, S., On K 1 and K 2 of algebraic surfaces. Special issue in honor of Hyman Bass on his seventieth birthday. Part I , K-Theory 30(1) (2003), 3769.
[M] Müller-Stach, S. J., Constructing indecomposable motivic cohomology classes on algebraic surfaces , J. Algebraic Geom. 6(3) (1997), 513543.
[PSt] Peters, C. and Steenbrink, J. H. M., Mixed Hodge Structures, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, A Series of Modern Surveys in Mathematics, Springer, 2010.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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