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OP-11364Status unassessedAlgebra

When is AA "geometrically X"? · Question 14.1

Noncommutative surfaces and Artin's conjecture · AIMPL workshop record

MSC 16 · Associative rings and algebras

Editorial mapping of AIMPL list topic: Noncommutative surfaces and Artin's conjecture. http://aimpl.org/ncsurfaceartin/ Not an author-supplied MSC code.

Workshop record · status unassessedAs of 2026-09-10 source snapshot; not a current-status certificationSource & evidence ↓
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Problem statement

Let RR be a commutative domain (finitely generated over Z\mathbb{Z}?) and let AA be a finitely presented RR-algebra. If X is some property, we say that AA is "geometrically X" if A⊗RQ(R)‾A \otimes_R \overline{Q(R)} has property X. Does there exists a dense constructible U⊆Spec RU \subseteq \text{Spec } R such that, for all p∈U\mathfrak{p} \in U, A⊗RQ(R/p)A \otimes_R Q(R/\mathfrak{p}) has property X?

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References
  1. [1]Noncommutative surfaces and Artin's conjecture · Original question link
  2. [2]AIMPL source bibliography link
  3. [3]AIMPL text license · CC BY-SA 3.0 linkAIM Problem Lists (AIMPL), original contributors; CC BY-SA 3.0. Adaptation: structural TeX converted to Markdown, documented source macros expanded, and source bibliography links added. Mathematical wording retained. These adapted source texts remain under CC BY-SA 3.0.

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