Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields / / Lisa Berger [and seven others]

• Autore: Berger Lisa <1969->
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , [2020]; ©2020
• Descrizione fisica: 1 online resource (144 pages)
• Disciplina: 516.352
• Soggetto topico: Curves, Algebraic; Legendre's functions; Rational points (Geometry); Birch-Swinnerton-Dyer conjecture; Jacobians; Abelian varieties; Finite fields (Algebra)
• Classificazione: 11G1011G3011G4014G0514G2514K15
• Persona (resp. second.): HallChris <1975->; PannekoekRené; ParkJennifer Mun Young; PriesRachel <1972->; SharifShahed <1977->; SilverbergAlice; UlmerDouglas <1960->
• Note generali: "Forthcoming, volume 266, number 1295."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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.
• Sommario/riassunto: "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)"--
• Titolo autorizzato: Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields
• ISBN: 1-4704-6253-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910794334103321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; Number 1295.