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7. Algebras birational to the Sklyanin algebra


    1. Add remark

      Problem 7.1.

      [Sue Sierra] Suppose that $D$ is a division ring of transcendence degree 2 with a unique valuation $\nu$ such that $\mathcal{O}_\nu/\mathfrak{m}_\nu = k(E)$, where $E$ is an elliptic curve. Suppose that there exists $x \in D$ with $\nu(x) = 1$ and that conjugation by $x$ induces a nontrivial translation $\sigma$ on $E$. Is $D$ isomorphic to $Q_{\text{gr}}(\text{Skl}(E,\sigma))_0$.

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