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Ordinary elliptic curves of high rank over $ar F_p(x)$ with constant j-invariant | | Irene I. Bouw
; Claus Diem
; Jasper Scholten
; | | Date: |
4 May 2003 | | Subject: | Number Theory; Algebraic Geometry MSC-class: 11G05 (Primary); 11G20; 14H40; 14H52 (Secondary) | math.NT math.AG | | Abstract: | We show that under the assumption of Artin’s Primitive Root Conjecture, for all primes p there exist ordinary elliptic curves over $ar F_p(x)$ with arbitrary high rank and constant j-invariant. For odd primes p, this result follows from a theorem which states that whenever p is a generator of (Z/ell Z)^*/<-1> (ell an odd prime) there exists a hyperelliptic curve over $ar F_p$ whose Jacobian is isogenous to a power of one ordinary elliptic curve. | | Source: | arXiv, math.NT/0305064 | | Services: | Forum | Review | PDF | Favorites | |
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