Algebraic dependence and Milnor K-theory
Adam Topaz
TL;DR
This paper demonstrates that algebraic dependence relations are reflected in Milnor K-theory of fields and shows that a field's isomorphism type is largely determined by its Milnor K-theory.
Contribution
It establishes a connection between algebraic dependence and Milnor K-theory and shows that the isomorphism type of a field can be recovered from its Milnor K-theory.
Findings
Algebraic dependence is encoded in Milnor K-theory.
The isomorphism type of a field is determined by its Milnor K-theory, up to purely inseparable extensions.
Abstract
This paper shows that algebraic (in)dependence is encoded in Milnor K-theory of fields. As an application, we show that the isomorphism type of a field is determined by its Milnor K-theory, up to purely inseparable extensions, in most situations.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology