Cyclic covers of the projective line, their jacobians and endomorphisms
نویسندگان
چکیده
منابع مشابه
Cyclic Covers of the Projective Line, Their Jacobians and Endomorphisms
ζp ∈ C. Let Q(ζp) be the pth cyclotomic field. It is well-known that Q(ζp) is a CM-field. If p is a Fermat prime then the only CM-subfield of Q(ζp) is Q(ζp) itself, since the Galois group of Q(ζp)/Q is a cyclic 2-group, whose only element of order 2 acts as the complex conjugation. All other subfields of Q(ζp) are totally real. Let f(x) ∈ C[x] be a polynomial of degree n ≥ 5 without multiple ro...
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Suppose K is a field of characteristic zero, Ka is its algebraic closure, f(x) ∈ K[x] is an irreducible polynomial of degree n ≥ 5, whose Galois group coincides either with the full symmetric group Sn or with the alternating group An. Let q be a power prime, Pq(t) = t q −1 t−1 . Let C be the superelliptic curve y = f(x) and J(C) its jacobian. We prove that if p does not divide n then the algebr...
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Suppose K is a eld of characteristic 0, Ka is its algebraic closure, p is an odd prime. Suppose, f(x) 2 K[x] is a polynomial of degree n 5 without multiple roots. Let us consider a curve C : y = f(x) and its jacobian J(C). It is known that the ring End(J(C)) of all Ka-endomorphisms of J(C) contains the ring Z[ p] of integers in the pth cyclotomic eld (generated by obvious automorphisms of C). W...
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We develop a general method for bounding Mordell-Weil ranks of Jacobians of arbitrary curves of the form y = f(x). As an example, we compute the Mordell-Weil ranks over Q and Q( √ −3) for a non-hyperelliptic curve of genus 8.
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Let K be a field of characteristic zero, n ≥ 5 an integer, f(x) an irreducible polynomial over K of degree n, whose Galois group contains a doubly transitive simple non-abelian group. Let p be an odd prime, Z[ζp] the ring of integers in the pth cyclotomic field, Cf,p : y p = f(x) the corresponding superelliptic curve and J(Cf,p) its jacobian. Assuming that either n = p + 1 or p does not divide ...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2002
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crll.2002.030