Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields [electronic resource] / Lisa Berger, Chris Hall, Rene Pannekoek, Jennifer Park, Rachel Pries, Shahed Sharif, Alice Silverberg, Douglas Ulmer.

"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...

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Bibliographic Details
Main Authors: Berger, Lisa, 1969- (Author)
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)
Language:English
Published: Providence, RI : American Mathematical Society, [2020]
Series:Memoirs of the American Mathematical Society, number 1295
Subjects:
Curves, Algebraic.
Abelian varieties.
Jacobians.
Birch-Swinnerton-Dyer conjecture.
Rational points (Geometry)
Legendre's functions.
Finite fields (Algebra)
Online Access:
ProQuest Ebook Central - Academic Complete: 2020 (Ebook Central @ Proquest)
Format: Electronic eBook
Contents:
  • The curve, explicit divisors, and relations
  • Descent calculations
  • Minimal regular model, local invariants, and domination by a product of curves
  • Heights and the visible subgroup
  • The L-function and the BSD conjecture
  • Analysis of J[p] and NS(Xd)tor
  • Index of the visible subgroup and the Tate-Shafarevich group
  • Monodromy of ℓ-torsion and decomposition of the Jacobian.