A CONSTRUCTION OF SURFACES WITH LARGE HIGHER CHOW GROUPS. (16th December 2019) - TERASOMA, TOMOHIDE
Abstract : In this paper, we construct surfaces in $P^{3}$ 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.