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14. When is $A$ "geometrically X"?


    1. Add remark

      Problem 14.1.

      [Jason Bell] Let $R$ be a commutative domain (finitely generated over $\mathbb{Z}$?) and let $A$ be a finitely presented $R$-algebra. If X is some property, we say that $A$ is "geometrically X" if $A \otimes_R \overline{Q(R)}$ has property X. Does there exists a dense constructible $U \subseteq \text{Spec } R$ such that, for all $\mathfrak{p} \in U$, $A \otimes_R Q(R/\mathfrak{p})$ has property X?
        1. Remark. [Jason Bell] Possible examples of X: noetherian, domain, prime, finite global dimension, $\text{p.dim } A = n$ over $A \otimes_R A^{\text{op}}$, etc.

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