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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 O_n and simple adjoint groups of type G_2 in the characteristic 2 case.

  • Subjects / Keywords
  • Graduation date
    2013-11
  • 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.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Chernousov, Vladimir (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Pianzola, Arturo (Mathematical and Statistical Sciences)
    • Zainoulline, Kirill (Mathematics and Statistics - University of Ottawa)
    • Putkaradze, Vakhtang (Mathematical and Statistical Sciences)
    • Gille, Stefan (Mathematical and Statistical Sciences)
    • Chernousov, Vladimir (Mathematical and Statistical Sciences)
    • Kuttler, Jochen (Mathematical and Statistical Sciences)