Milnor K-theory of rings,higher Chow groups and applications |
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Authors: | Philippe Elbaz-Vincent Stefan Müller-Stach |
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Affiliation: | 1.Laboratoire G.T.A., UMR CNRS 5030, CC 51, U. Montpellier II, 34095 Montpellier Cedex 5, France (e-mail: pev@math.univ-monpt2.fr),FR;2.Fachbereich 6 Mathematik, Universit?t GH Essen, 45117 Essen, Deutschland (e-mail: mueller-stach@uni-essen.de),DE |
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Abstract: | If R is a smooth semi-local algebra of geometric type over an infinite field, we prove that the Milnor K-group K M n (R) surjects onto the higher Chow group CH n (R , n) for all n≥0. Our proof shows moreover that there is an algorithmic way to represent any admissible cycle in CH n (R , n) modulo equivalence as a linear combination of “symbolic elements” defined as graphs of units in R. As a byproduct we get a new and entirely geometric proof of results of Gabber, Kato and Rost, related to the Gersten resolution for the Milnor K-sheaf. Furthermore it is also shown that in the semi-local PID case we have, under some mild assumptions, an isomorphism. Some applications are also given. Oblatum 17-XII-1998 & 1-X-2001?Published online: 18 January 2002 |
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