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Permanent link (DOI): https://doi.org/10.7939/R3VX06B59

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Height Pairing on Graded Pieces of a Bloch-Beilinson Filtration Open Access

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Other title
Subject/Keyword
Height Pairing
Bloch-Beilinson Filtration
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Goswami, Souvik
Supervisor and department
Lewis, James (Department of Mathematical and Statistical Sciences)
Examining committee member and department
Lewis, James (Department of Mathematical and Statistical Sciences)
Doran, Charles (Department of Mathematical and Statistical Sciences)
Lau, Anthony (Department of Mathematical and Statistical Sciences)
Favero, David (Department of Mathematical and Statistical Sciences)
Chen, Xi (Department of Mathematical and Statistical Sciences)
Pedrini, Claudio (University of Genova)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2015-01-19T13:25:56Z
Graduation date
2015-06
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
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projective variety defined over a field of finite transcendence degree over a number field, the folklore conjecture is no longer valid.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.
Language
English
DOI
doi:10.7939/R3VX06B59
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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