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
DOI: https://doi.org/10.1090/S1056-3911-09-00514-1
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
Email: moritz.kerz@mathematik.uni-regensburg.de

DOI: https://doi.org/10.1090/S1056-3911-09-00514-1
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.

American Mathematical Society