Non-supersingular hyperelliptic jacobians
نویسندگان
چکیده
منابع مشابه
Non-supersingular Hyperelliptic Jacobians
In his previous papers [25, 26, 28] the author proved that in characteristic 6= 2 the jacobian J(C) of a hyperelliptic curve C : y = f(x) has only trivial endomorphisms over an algebraic closure Ka of the ground field K if the Galois group Gal(f) of the irreducible polynomial f(x) ∈ K[x] is either the symmetric group Sn or the alternating group An. Here n ≥ 9 is the degree of f . The goal of th...
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We present a method to solve in an efficient way the problem of constructing the curves given by Torelli’s theorem in dimension 3 over the complex numbers: For an absolutely simple principally polarized abelian threefold A over C given by its period matrix Ω, compute a model of the curve of genus three (unique up to isomorphism) whose Jacobian, equipped with its canonical polarization, is isomo...
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In [17] the author proved that in characteristic 0 the jacobian J(C) = J(Cf ) of a hyperelliptic curve C = Cf : y 2 = f(x) has only trivial endomorphisms over an algebraic closure Ka of the ground field K if the Galois group Gal(f) of the irreducible polynomial f ∈ K[x] is “very big”. Namely, if n = deg(f) ≥ 5 and Gal(f) is either the symmetric group Sn or the alternating group An then the ring...
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Let K be a field of characteristic different from 2, and let f(x) be a sextic polynomial irreducible over K with no repeated roots, whose Galois group is A5. If the Jacobian of the hyperelliptic curve y = f(x) admits real multiplication over the ground field from an order of a real quadratic number field, then either its endomorphism algebra is this quadratic field or the Jacobian is supersingu...
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Many interesting questions can be asked about the decomposition of Jacobians of curves. For instance, we may want to know which curves have completely decomposable Jacobians (Jacobians which are the product of g elliptic curves) [4]. We may ask about number theoretic properties of the elliptic curves that show up in the decomposition of Jacobians of curves [2]. We would also like to know how ma...
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ژورنال
عنوان ژورنال: Bulletin de la Société mathématique de France
سال: 2004
ISSN: 0037-9484,2102-622X
DOI: 10.24033/bsmf.2477