In this paper we discuss the Brauer group of a field and its connections with cohomology groups. Definitions involving central simple algebras lead to a discussion of splitting fields, which are the important step in the connection of the Brauer group with cohomology groups. Finally, once the connection between the Brauer group and cohomology groups is established, the paper finishes by calculating specific examples of cocycles associated to certain classes of central simple algebras.

Author Bio

Jon Aycock graduated from the University of North Carolina at Chapel Hill in 2016, where he majored in math. In September of that year, he began a Ph.D. program at the University of Oregon. His interests lie in abstract algebra, particularly algebraic geometry. In his free time, he likes to play ultimate frisbee and board games.