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Permanent link (DOI): https://doi.org/10.7939/R3KK94M3K

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Normal Functions and the Bloch-Beilinson Filtration Open Access

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Other title
Subject/Keyword
hodge theory
Bloch-Beilinson Filtration
chow groups
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Méndez Dávila, Héctor Damián
Supervisor and department
James Lewis (Mathematical and Statistical Sciences)
Examining committee member and department
James Lewis (Mathematical and Statistical Sciences)
Xi Chen (Mathematical and Statistical Sciences)
Charles Doran (Mathematical and Statistical Sciences)
David Favero (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2015-01-20T13:23:21Z
Graduation date
2015-06
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
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.
Language
English
DOI
doi:10.7939/R3KK94M3K
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. 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.
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