Lower Bounds for Essential Dimension of Algebraic Groups in the Characteristic 2 Case

• Author / Creator

  Babic, Antonio Alain

• When computing the essential dimension of an algebraic group G defined over a field k, finding lower bounds is generally a much more difficult problem than finding upper bounds. For simple algebraic groups G of adjoint type, Chernousov-Serre developed a general method for computing lower bounds of G via an orthogonal representation. Their work did not cover the case when char(k) = 2, but they did note their belief that the method could be extended to this case. We will show that the method developed by Chernousov-Serre does indeed work in the characteristic 2 case. As an application, we employ the method to assist with the computation of the essential dimension of the orthogonal group On and simple adjoint groups of type G2 in the characteristic 2 case.

• Subjects / Keywords

  • Essential Dimension
  • Algebraic Groups

• Graduation date

  Fall 2013

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R31V5BN7Q

• 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.