Rank one Drinfeld modules on hyperelliptic curves
نویسندگان
چکیده
منابع مشابه
Rank-one Drinfeld Modules on Elliptic Curves
The sgn-normalized rank-one Drinfeld modules 4> associated with all elliptic curves E over ¥q for 4 < q < 13 are computed in explicit form. (Such 4> for q < 4 were computed previously.) These computations verify a conjecture of Dormán on the norm of j{) = aq+l and also suggest some interesting new properties of . We prove Dorman's conjecture in the ramified case. We also prove the formula...
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We prove that the curve Y0(p) has no F2(T )-rational points where p ⊳ F2[T ] is a prime ideal of degree at least 3 and Y0(p) is the affine Drinfeld modular curve parameterizing Drinfeld modules of rank two over F2[T ] of general characteristic with Hecke-type level p-structure. As a consequence we derive a conjecture of Schweizer describing completely the torsion of Drinfeld modules of rank two...
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Let φ be a Drinfeld module of rank 2 over the field of rational functions F = Fq(T ), with EndF̄ (φ) = Fq[T ]. Let K be a fixed imaginary quadratic field over F and d a positive integer. For each prime p of good reduction for φ, let πp(φ) be a root of the characteristic polynomial of the Frobenius endomorphism of φ over the finite field Fq[T ]/p. Let Πφ(K; d) be the number of primes p of degree ...
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We derive asymptotically optimal upper bounds on the number of L-rational torsion points on a given elliptic curve or Drinfeld module defined over a finitely generated field K, as a function of the degree [L : K]. Our main tool is the adelic openness of the image of Galois representations attached to elliptic curves and Drinfeld modules, due to Serre and Pink-Rütsche, respectively. Our approach...
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We assemble and reorganize the recent work in the area of hyperelliptic pairings: We survey the research on constructing hyperelliptic curves suitable for pairing-based cryptography. We also showcase the hyperelliptic pairings proposed to date, and develop a unifying framework. We discuss the techniques used to optimize the pairing computation on hyperelliptic curves, and present many direction...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1995
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700014465