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010 a| 2020032015;

020 a| 9781470442194q| (paperback);

020 z| 9781470462536q| (pdf);

035 a| (WaSeSS)ssj0002463573;

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050 00 a| QA565b| .B47 2020;

082 00 a| 516.3/532| 23;

084 a| 11G10a| 11G30a| 11G40a| 14G05a| 14G25a| 14K152| msc;

100 1 a| Berger, Lisa,d| 1969-?| UNAUTHORIZED;

245 10 a| Explicit arithmetic of Jacobians of generalized Legendre curves over global function fieldsh| [electronic resource] /c| Lisa Berger, Chris Hall, Rene Pannekoek, Jennifer Park, Rachel Pries, Shahed Sharif, Alice Silverberg, Douglas Ulmer.;

260 a| Providence, RI :b| American Mathematical Society,c| [2020];

300 a| v, 131 pages :b| illustrations ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| number 1295;

500 a| "Forthcoming, volume 266, number 1295.";

504 a| Includes bibliographical references.;

505 0 a| 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.;

506 a| Available only to authorized users.;

520 a| "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)"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Curves, Algebraic.=| ^A43161;

650 0 a| Abelian varieties.=| ^A68270;

650 0 a| Jacobians.=| ^A80312;

650 0 a| Birch-Swinnerton-Dyer conjecture.=| ^A572796;

650 0 a| Rational points (Geometry)=| ^A515357;

650 0 a| Legendre's functions.=| ^A276381;

650 0 a| Finite fields (Algebra)=| ^A72195;

650 7 a| Number theory -- Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx] -- Abelian varieties of dimension $> 1$ [See also 14Kxx].2| msc;

650 7 a| Number theory -- Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx] -- Curves of arbitrary genus or genus $\ne 1$ over global fields [See also 14H25].2| msc;

650 7 a| Number theory -- Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx] -- $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]2| msc;

650 7 a| Algebraic geometry -- Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx] -- Rational points.2| msc;

650 7 a| Algebraic geometry -- Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx] -- Global ground fields.2| msc;

650 7 a| Algebraic geometry -- Abelian varieties and schemes -- Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx].2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Hall, Chris,d| 1975-?| UNAUTHORIZED;

700 1 a| Pannekoek, René.?| UNAUTHORIZED;

700 1 a| Park, Jennifer Mun Young.?| UNAUTHORIZED;

700 1 a| Pries, Rachel,d| 1972-?| UNAUTHORIZED;

700 1 a| Sharif, Shahed,d| 1977-?| UNAUTHORIZED;

700 1 a| Silverberg, Alice.=| ^A1059214;

700 1 a| Ulmer, Douglas,d| 1960-?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6346635;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5684848-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 9/17/2021x| EBOOKz| HERESOURCE;

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

Author/creator	Berger, Lisa, 1969-
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, [2020]
Description	v, 131 pages : illustrations ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Curves, Algebraic. Abelian varieties. Jacobians. Birch-Swinnerton-Dyer conjecture. Rational points (Geometry) Legendre's functions. Finite fields (Algebra)

Other author/creator	Hall, Chris, 1975-
Other author/creator	Pannekoek, René.
Other author/creator	Park, Jennifer Mun Young.
Other author/creator	Pries, Rachel, 1972-
Other author/creator	Sharif, Shahed, 1977-
Other author/creator	Silverberg, Alice.
Other author/creator	Ulmer, Douglas, 1960-
Series	Memoirs of the American Mathematical Society, 0065-9266 ; number 1295
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.
Abstract	"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.
General note	"Forthcoming, volume 266, number 1295."
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2020032015
ISBN	9781470442194 (paperback)
ISBN	(pdf)

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

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