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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Milnor $K$-theory of local rings with finite residue fields

Author: Moritz Kerz
Journal: J. Algebraic Geom. 19 (2010), 173-191
Published electronically: July 9, 2009
MathSciNet review: 2551760
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Abstract | References | Additional Information

Abstract: We propose a definition of improved Milnor $K$-groups of local rings with finite residue fields, such that the improved Milnor $K$-sheaf in the Zariski topology is a universal extension of the naive Milnor $K$-sheaf with a certain transfer map for étale extensions of local rings. The main theorem states that the improved Milnor $K$-ring is generated by elements of degree one.

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Additional Information

Moritz Kerz
Affiliation: NWF I-Mathematik, Universität Regensburg, 93040 Regensburg, Germany

Received by editor(s): October 12, 2007
Received by editor(s) in revised form: January 30, 2008
Published electronically: July 9, 2009
Additional Notes: The author is supported by Studienstiftung des deutschen Volkes.