Hidden Bibliographic Details
| Other authors / contributors: | Hall, Chris, 1975- author.
Pannekoek, René, author.
Park, Jennifer Mun Young, author.
Pries, Rachel, 1972- author.
Sharif, Shahed, 1977- author.
Silverberg, Alice, author.
Ulmer, Douglas, 1960- author.
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| ISBN: | 9781470442194
1470442191
9781470462536
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| Notes: | "Forthcoming, volume 266, number 1295."
Includes bibliographical references.
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| Summary: | "We study the Jacobian J of the smooth projective curve C of genus r-1 with affine model yr = xr-1(x+ 1)(x + t) over the function field Fp(t), when p is prime and r [greater than or equal to] 2 is an integer prime to p. When q is a power of p and d is a positive integer, we compute the L-function of J over Fq(t1/d) and show that the Birch and Swinnerton-Dyer conjecture holds for J over Fq(t1/d). When d is divisible by r and of the form p[nu] + 1, and Kd := Fp([mu]d, t1/d), we write down explicit points in J(Kd), show that they generate a subgroup V of rank (r-1)(d-2) whose index in J(Kd) is finite and a power of p, and show that the order of the Tate-Shafarevich group of J over Kd is [J(Kd) : V ]2. When r > 2, we prove that the "new" part of J is isogenous over Fp(t) to the square of a simple abelian variety of dimension [phi](r)/2 with endomorphism algebra Z[[mu]r]+. For a prime with pr, we prove that J[](L) = {0} for any abelian extension L of Fp(t)"--
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