Differential graded Brauer groups over dg-rings

TL;DR

This paper introduces a Brauer group concept for differential graded algebras over dg-rings, providing explicit classifications and computations for dg-fields.

Contribution

It defines a new Brauer group for dg-algebras over dg-rings and offers explicit classifications and calculations for dg-fields.

Findings

Explicit classification of dg-fields.

Computed the Brauer group for each case.

Provided a new framework for dg-algebra classification.

Abstract

We define a Brauer group for differential graded algebras over differential graded graded-commutative or commutative base rings. Based on previous work we give an explicit classification of dg-fields, and compute the so-defined Brauer group in each case explicitly.