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...
متن کاملThe Rank of the Cartier Operator on Cyclic Covers of the Projective Line
We give a lower bound on the rank of the Cartier operator of Jacobian varieties of hyperelliptic and superelliptic curves in terms of their genus.
متن کاملThe Endomorphism Rings of Jacobians of Cyclic Covers of the Projective Line
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...
متن کاملField of moduli versus field of definition for cyclic covers of the projective line
We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli R that can not be defined over R is also given.
متن کاملExplicit Descent for Jacobians of Cyclic Covers of the Projective Line
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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ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2006
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-006-0028-4