Normal Functions and the Bloch-Beilinson Filtration

  • Author / Creator
    Méndez Dávila, Héctor Damián
  • Let $X/k$ be a smooth projective geometrically irreducible variety over a field $k$, and $\CH^r(X;\Q) := \CH^r(X)\otimes\Q$ the Chow group of codimension $r$ cycles, modulo rational equivalence. A long standing conjecture, due by S. Bloch and fortified by A. Beilinson, is the existence of a descending filtration on $\CH^r(X;\Q)$, whose graded pieces detect the complexity of $\CH^r(X;\Q)$. The question then is whether one can provide an explicit geometric interpretation of this filtration in the situation where $k\subseteq \C$ is a subfield. This will involve a candidate filtration introduced by Lewis, the concept of cycle induced normal functions, and fields of definition of their zero locus. Towards this goal, we present some partial results, and new lines of enquiry.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • 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
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • James Lewis (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • David Favero (Mathematical and Statistical Sciences)
    • Charles Doran (Mathematical and Statistical Sciences)
    • Xi Chen (Mathematical and Statistical Sciences)
    • James Lewis (Mathematical and Statistical Sciences)