Local-global properties of torsion points on three-dimensional abelian varieties
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...
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2005
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ndltd-UMASS-oai-scholarworks.umass.edu-dissertations-40612020-12-02T14:36:26Z Local-global properties of torsion points on three-dimensional abelian varieties Cullinan, John 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. 2005-01-01T08:00:00Z text https://scholarworks.umass.edu/dissertations/AAI3179867 Doctoral Dissertations Available from Proquest ENG ScholarWorks@UMass Amherst Mathematics |
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NDLTD |
| language |
ENG |
| sources |
NDLTD |
| topic |
Mathematics |
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Mathematics Cullinan, John Local-global properties of torsion points on three-dimensional abelian varieties |
| description |
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. |
| author |
Cullinan, John |
| author_facet |
Cullinan, John |
| author_sort |
Cullinan, John |
| title |
Local-global properties of torsion points on three-dimensional abelian varieties |
| title_short |
Local-global properties of torsion points on three-dimensional abelian varieties |
| title_full |
Local-global properties of torsion points on three-dimensional abelian varieties |
| title_fullStr |
Local-global properties of torsion points on three-dimensional abelian varieties |
| title_full_unstemmed |
Local-global properties of torsion points on three-dimensional abelian varieties |
| title_sort |
local-global properties of torsion points on three-dimensional abelian varieties |
| publisher |
ScholarWorks@UMass Amherst |
| publishDate |
2005 |
| url |
https://scholarworks.umass.edu/dissertations/AAI3179867 |
| work_keys_str_mv |
AT cullinanjohn localglobalpropertiesoftorsionpointsonthreedimensionalabelianvarieties |
| _version_ |
1719365295590604800 |