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A CONSTRUCTION OF SURFACES WITH LARGE HIGHER CHOW GROUPS

Part of: Cycles and subschemes $K$-theory in geometry

Published online by Cambridge University Press:  16 October 2018

TOMOHIDE TERASOMA
TOMOHIDE TERASOMA*
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-1-8 Komaba, Meguroku, Tokyo 153-8914, Japan email terasoma@ms.u-tokyo.ac.jp
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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.

MSC classification

Primary: 14C15: (Equivariant) Chow groups and rings; motives 19E15: Algebraic cycles and motivic cohomology 14C30: Transcendental methods, Hodge theory , Hodge conjecture
Type
Article
Information
Nagoya Mathematical Journal , Volume 236: Celebrating the 60th Birthday of Shuji Saito , December 2019 , pp. 311 - 331
Copyright
© 2018 Foundation Nagoya Mathematical Journal  

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References

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