A Specific Construction of a Versal Torsor under a Finite Group G

• Author / Creator

  Zeng, Zhaowei

• Versal torsors arise as an important tool in algebraic groups and algebraic geometry for the universal perspective they provide on the behaviour and properties of other torsors under the same group. Two classic examples of versal torsors are con- structed from general linear groups and affine spaces, respectively, described in lecture notes of Jean-Pierre Serre. The objective of this thesis is to find an algebraic proof for the second construction under finite groups without the use of heavy machinery from Galois cohomology.
  The content of the different chapters is as follows:
  Chapter 1 is an introduction to the goals of the thesis.
  Chapter 2 is dedicated to give the readers a comprehensive introduction to
  ́etale algebras and Galois algebras.
  Chapter 3 and 4 are general discussions on quotients of varieties and torsors,
  respectively, followed by their behaviour in our special case.
  Chapter 5 presents two classic constructions of versal torsors under finite
  groups and lastly gives a new proof for the construction from affine spaces.

• Subjects / Keywords

  • Torsor
  • Versal torsor
  • Étale algebra
  • Galois algebra

• Graduation date

  Spring 2024

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-8w1b-sg25

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.