Lisa Berger,Chris Hall,Rene Pannekoek,Rachel Pries,Shahed Sharif
Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
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Excellent- More about Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields
The authors study the Jacobian $J$ of a smooth projective curve over a function field, proving the Birch and Swinnerton-Dyer conjecture for certain values of $q$ and $d$.
Format: Paperback / softback
Length: 131 pages
Publication date: 30 October 2020
Publisher: American Mathematical Society
The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $\mathbb F_p(t)$, when $p$ is prime and $r\ge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $\mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $\mathbb F_q(t^1/d)$.
Weight: 270g
Dimension: 177 x 253 x 11 (mm)
ISBN-13: 9781470442194
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