01800nas a2200361 i 450099100281640970753620231114120406.0011205m19612002ii || | |eng 0581-5738b11712041-39ule_instPERLE008006ExLCDU 311.312Sankhya. Series BSankhya. Series B :Indian journal of statistics /Indian Statistical Institute Calcutta,1961-2002.In the year 1974 gives rise to: Sankhya. Series C. Sample surveys. Theory and practice.Absorbes from the year 1981: Sankhya. Series C. Sample surveys. Theory and practice and Sankhya. Series D. Quantitative economics.Merged with: Sankhya. Series A, from the year 2003, to form: Sankhya. The Indian Journal of StatisticsCodice CNR: P 00017387LE013 1961-1969; 1974-2002. lac.: 1961; 1991;1998;2002;LE025 1999-2002;Indian Statistical Instituteauthorhttp://id.loc.gov/vocabulary/relators/aut503926Sankhya : The Indian journal of statisticsSankhya. The Indian Journal of Statistics [2003].b1171204107-02-2208-07-02991002816409707536LE0131le013-E0.00-no 180000.i1194869308-07-02LE013Vol. 64 (2002)1le013nE64.29-no 180000.i1281786721-10-03LE0251le025-E0.00-no 180000.i1194870x08-07-02LE0251le025Abbonamento 2003nE55.00-no 180000.i1257077124-09-03Sankhya. Series B1453710UNISALENTO(3)le013(2)le02501-01-01sa -engii 0503673nam 2200697 450 991081354600332120201204082343.01-4704-6253-2(CKB)4100000011437433(MiAaPQ)EBC6346635(RPAM)21697713(PPN)250799235(EXLCZ)99410000001143743320201204d2020 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierExplicit arithmetic of Jacobians of generalized Legendre curves over global function fields /Lisa Berger [and seven others]Providence, Rhode Island :American Mathematical Society,[2020]©20201 online resource (144 pages)Memoirs of the American Mathematical Society ;Number 1295"Forthcoming, volume 266, number 1295."1-4704-4219-1 Includes bibliographical references.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."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)"--Provided by publisher.Memoirs of the American Mathematical Society ;Number 1295.Curves, AlgebraicLegendre's functionsRational points (Geometry)Birch-Swinnerton-Dyer conjectureJacobiansAbelian varietiesFinite fields (Algebra)Curves, Algebraic.Legendre's functions.Rational points (Geometry)Birch-Swinnerton-Dyer conjecture.Jacobians.Abelian varieties.Finite fields (Algebra)516.35211G1011G3011G4014G0514G2514K15mscBerger Lisa1969-1686950Hall Chris1975-Pannekoek RenéPark Jennifer Mun YoungPries Rachel1972-Sharif Shahed1977-Silverberg AliceUlmer Douglas1960-MiAaPQMiAaPQMiAaPQBOOK9910813546003321Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields4060057UNINA