Milnor K_2 and field homomorphisms

TL;DR

This paper demonstrates that for algebraic varieties of dimension greater than one over an algebraically closed field of characteristic zero, their function fields can be uniquely identified using their first and second Milnor K-groups.

Contribution

It establishes a new characterization of function fields via Milnor K-groups, linking algebraic K-theory to geometric properties of varieties.

Findings

Function fields are determined by Milnor K_1 and K_2 groups.

First and second Milnor K-groups suffice for classification.

Results apply to varieties over algebraically closed fields of characteristic zero.

Abstract

We prove that the function field of an algebraic variety of dimension greater than 1 over an algebraically closed field of characteristic zero is determined by its first and second Milnor K-groups.