Picard schemes of noncommutative bielliptic surfaces

TL;DR

This paper investigates the Brauer group of bielliptic surfaces, constructing Azumaya algebras to explore the noncommutative Picard scheme and its properties, revealing new insights into their algebraic structure.

Contribution

It introduces a detailed analysis of the noncommutative Picard scheme for Azumaya algebras on bielliptic surfaces, highlighting novel structural properties.

Findings

Realization of Brauer group elements as Azumaya algebras

Analysis of the noncommutative Picard scheme properties

Insights into the algebraic structure at the generic point

Abstract

We study the nontrivial elements in the Brauer group of a bielliptic surface and show that they can be realized as Azumaya algebras with a simple structure at the generic point of the surface. We go on to study some properties of the noncommutative Picard scheme associated to such an Azumaya algebra.