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9. Division rings of GK-transcendence 2


    1. Add remark

      Problem 9.1.

      [Paul Smith] Suppose that $D$ is a finitely generated division algebra over a finite field $k$ of GK-transcendence degree 2. Is $D$ PI (or finite over its centre)?
        1. Remark. Smoktunowicz shows that this is true if $D=Q(R)$ where $R$ is a finitely generated $k$-algebra with quadratic growth and $Z(R)$ is infinite.

              Cite this as: AimPL: Noncommutative surfaces and Artin's conjecture, available at http://aimpl.org/ncsurfaceartin.