Abstract/Details

Local-global properties of torsion points on three-dimensional abelian varieties


2005 2005

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Abstract (summary)

Let A be an abelian variety over a number field K, and let ℓ be a prime number. If A has a K-rational ℓ-torsion point, then for almost finite places [special characters omitted] of K, A has an ℓ-torsion point mod [special characters omitted]. Katz has shown that the converse is true if the dimension of A is less than three, and has exhibited specific counterexamples when A has dimension greater than or equal to three. Using the subgroup structure of the finite symplectic group, we classify those abelian threefolds which violate this local-global principle for ℓ-torsion points; some geometric realizations of these obstructions are provided.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Abelian varieties; Torsion points
Title
Local-global properties of torsion points on three-dimensional abelian varieties
Author
Cullinan, John
Number of pages
116
Publication year
2005
Degree date
2005
School code
0118
Source
DAI-B 66/06, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780542197536, 0542197537
Advisor
Wong, Siman
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3179867
ProQuest document ID
304999661
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304999661
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