Height Pairing on Graded Pieces of a Bloch-Beilinson Filtration

• Author / Creator

  Goswami, Souvik

• For a smooth projective variety defined over a number field, Beilinson (and independently Bloch) constructed a `height' pairing under very reasonable assumptions and with a number of conjectural properties. A folklore conjecture related to this pairing states that the rational Griffiths Abel-Jacobi map is injective. But for a smooth projective variety defined over a field of finite transcendence degree over a number field, the folklore conjecture is no longer valid. Instead we have the concept of a conjectural Bloch-Beilinson filtration, a candidate for which was given by James Lewis. Under some standard assumptions, the main point of this thesis is to generalize the height pairing to the graded pieces of this candidate Bloch-Beilinson filtration using cohomological machinery.

• Subjects / Keywords

  • Bloch-Beilinson Filtration
  • Height Pairing

• Graduation date

  Spring 2015

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3VX06B59

• 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.