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- Genus one curves from division algebras of degree 3
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Genus one curves from division algebras of degree 3 Saltman, David J
Description
If $D/F$ is a division algebra of degree 3, then the Severi-Brauer
variety of $D$, call it $X$, is a form of the projective plane.
The line bundle $O(3)$ is defined on $X$, which says it makes sense to talk
about cubic curves on $X$. Since $X$ has no rational points,
these are genus one curve and not elliptic curves. However,
they are principle homogeneous spaces over their Jacobians $E$, which are
elliptic curves. Which ones occur?
Item Metadata
| Title |
Genus one curves from division algebras of degree 3
|
| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2016-09-15T13:32
|
| Description |
If $D/F$ is a division algebra of degree 3, then the Severi-Brauer
variety of $D$, call it $X$, is a form of the projective plane.
The line bundle $O(3)$ is defined on $X$, which says it makes sense to talk
about cubic curves on $X$. Since $X$ has no rational points,
these are genus one curve and not elliptic curves. However,
they are principle homogeneous spaces over their Jacobians $E$, which are
elliptic curves. Which ones occur?
|
| Extent |
50 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: Center for Communications Research
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| Series | |
| Date Available |
2017-03-16
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0343252
|
| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
|
| Scholarly Level |
Other
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
|
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International