Skip to main content
Open Access Publications from the University of California


UCLA Electronic Theses and Dissertations bannerUCLA

Algebraic Tori and Essential Dimension

  • Author(s): Ruozzi, Anthony
  • Advisor(s): Merkurjev, Alexander
  • et al.

Interest in essential dimension problems has been growing over the past decade. In part, it is because the idea of essential dimension captures quite elegantly the problem of parametrizing a wide range of algebraic objects. But perhaps more, it is because the study of essential dimension requires most of the algebraic arsenal. What began as a problem in Galois cohomology and representation theory now has connections to versal torsors, stacks, motives, birational geometry, and invariant theory. This exposition will focus on just a small bit of this theory: algebraic tori and how they can be used to help us calculate the essential p-dimension for PGLn.

Main Content
Current View