Zero-cycles with modulus associated to hyperplane arrangements on affine spaces

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For a hyperplane arrangement on the affine n-space over k, we define and study a group of zero-cycles relative to , which is closely related to the relative Chow group of M. Kerz and S. Saito. We compute our cycle groups for a special kind of hyperplane arrangements, called polysimplicial spheres. We prove that they are isomorphic to the Milnor K-groups , similar to the theorem of Nesterenko-Suslin-Totaro. Using this result, we show that the Kerz-Saito relative Chow group does not necessarily vanish for , contrary to the result of Krishna-Park that for and , the group does vanish when k is a field of characteristic 0.
Publisher
SPRINGER HEIDELBERG
Issue Date
2018-01
Language
English
Article Type
Article
Keywords

HIGHER CHOW GROUPS; K-THEORY; SCHEMES; FIELD

Citation

MANUSCRIPTA MATHEMATICA, v.155, no.1-2, pp.15 - 45

ISSN
0025-2611
DOI
10.1007/s00229-017-0931-x
URI
http://hdl.handle.net/10203/239924
Appears in Collection
MA-Journal Papers(저널논문)
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