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[null,"1.","Record Nr.",null,"UNINA9910813546003321"]
[null,null,"Autore",null,"Berger Lisa <1969->"]
[null,null,"Titolo",null,"Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields / / Lisa Berger [and seven others]"]
[null,null,"Pubbl/distr/stampa",null,"Providence, Rhode Island : , : American Mathematical Society, , [2020]"]
[{"$nulls":4},"©2020"]
[null,null,"ISBN",null,"1-4704-6253-2"]
[null,null,"Descrizione fisica",null,"1 online resource (144 pages)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society ; ; Number 1295"]
[null,null,"Classificazione",null,"11G1011G3011G4014G0514G2514K15"]
[null,null,"Disciplina",null,"516.352"]
[null,null,"Soggetti",null,"Curves, Algebraic"]
[{"$nulls":4},"Legendre's functions"]
[{"$nulls":4},"Rational points (Geometry)"]
[{"$nulls":4},"Birch-Swinnerton-Dyer conjecture"]
[{"$nulls":4},"Jacobians"]
[{"$nulls":4},"Abelian varieties"]
[{"$nulls":4},"Finite fields (Algebra)"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","\"Forthcoming, volume 266, number 1295.\""]
[null,null,null,"Nota di bibliografia","Includes bibliographical references."]
[null,null,"Nota di contenuto",null,"The curve, explicit divisors, and relations -- Descent calculations -- Minimal regular model, local invariants, and domination by a product of curves -- Heights and the visible subgroup -- The L-function and the BSD conjecture -- Analysis of J[p] and NS(Xd)tor -- Index of the visible subgroup and the Tate-Shafarevich group -- Monodromy of ℓ-torsion and decomposition of the Jacobian."]
[null,null,null,"Sommario/riassunto","\"We study the Jacobian J of the smooth projective curve C of genus r-1 with affine model yr = xr-1(x+ 1)(x + t) over the function field Fp(t), when p is prime and r [greater than or equal to] 2 is an integer prime to p. When q is a power of p and d is a positive integer, we compute the L-function of J over Fq(t1/d) and show that the Birch and Swinnerton-Dyer conjecture holds for J over Fq(t1/d). When d is divisible by r and of the form p[nu] + 1, and Kd := Fp([mu]d, t1/d), we write down explicit points in J(Kd), show that they generate a subgroup V of rank (r-1)(d-2) whose index in J(Kd) is finite and a power of p, and show that the order of the Tate-Shafarevich group of J over Kd is [J(Kd) : V ]2. When r > 2, we prove that the \"new\" part of J is isogenous over Fp(t) to the square of a simple abelian variety of dimension [phi](r)/2 with endomorphism "]
[{"$nulls":4},"algebra Z[[mu]r]+. For a prime with pr, we prove that J[](L) = {0} for any abelian extension L of Fp(t)\"--"]