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13. Completions of division rings (Todo: ask Matt)


    1. Add remark

      Problem 13.1.

      [Matthew Satriano] Let $D$ be a division ring of transcendence degree 2 over $k$, where $D = Q_{\text{gr}}(A)_0$ for some graded algebra $A$. Assume $D$ has a valuations $\nu$ and that $A$ has cubic growth, and that $k \subseteq k(C) \subseteq \widehat{D}_\nu$. Does there exist $A$ such that...

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