| Register
\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

4. Colin’s problems


    1. Add remark

      Problem 4.1.

      [Colin Ingalls] Let $A$ be a graded algebra over a finite field satisfying Artin’s conditions which is birationally PI, i.e. $Q_{\text{gr}}(A)_0$ is PI. Find "weak" conditions $(*)$ so that the deformations (i.e. the lifts to characteristic 0) are also birationally PI.
        1. Remark. For example, what would $(*)$ be in the case that $A$ is an order of global dimension 2?


            • Add remark

              Problem 4.2.

              [Colin Ingalls] Let $A$ be as above over a field of characteristic 0 and reduce to a finite field. Find conditions $(\dagger)$ so that there exists such a reduction with (generically) good properties.

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