Generically Trivial Azumaya Algebras on a Rational Surface with a Non Rational Singularity

Abstract

Elementary examples are presented of normal algebraic surfaces X with singular points x such that at the local ring 𝒪 _{X, x} there exist Azumaya algebras of all orders in the Brauer group that are split by the field of rational functions on X. These algebra classes correspond to elements of torsion in the class group of the henselian local ring . The surfaces X are affine normal rational and the singularities x are nonrational.

Key Words:

• Azumaya algebras
• Brauer group
• Class group
• Non rational singularity
• Rational surface

2010 Mathematics Subject Classification:

• 16H05
• Secondary 14F22, 14J17, 14J26

Notes

Communicated by A. Wadsworth.