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Abelian varieties with prescribed embedding degree
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Freeman, David, Stevenhagen, Peter and Streng, Marco (2008) Abelian varieties with prescribed embedding degree. In: 8th international symposium, ANTS-VIII, Canada, 17-22 May 2008. Published in: Algorithmic number theory : 8th international symposium, ANTS-VIII, Banff, Canada, May 17-22, 2008 : proceedings pp. 60-73. doi:10.1007/978-3-540-79456-1_3 ISSN 9783540794561.
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Official URL: http://webcat.warwick.ac.uk:80/record=b2503218
Abstract
We present an algorithm that, on input of a CM-field K, aninteger k ≥ 1, and a prime r ≡ 1 mod k, constructs a q-Weil numberπ ∈ OK corresponding to an ordinary, simple abelian variety A overthe field F of q elements that has an F-rational point of order r andembedding degree k with respect to r. We then discuss how CM-methods over K can be used to explicitly construct A.
Item Type: | Conference Item (Paper) | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Algorithmic number theory : 8th international symposium, ANTS-VIII, Banff, Canada, May 17-22, 2008 : proceedings | ||||
Publisher: | Springer | ||||
ISSN: | 9783540794561 | ||||
Official Date: | 2008 | ||||
Dates: |
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Page Range: | pp. 60-73 | ||||
DOI: | 10.1007/978-3-540-79456-1_3 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Conference Paper Type: | Paper | ||||
Title of Event: | 8th international symposium, ANTS-VIII | ||||
Type of Event: | Conference | ||||
Location of Event: | Canada | ||||
Date(s) of Event: | 17-22 May 2008 |
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