Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields /
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| Author / Creator: | Berger, Lisa, 1969- author. |
|---|---|
| Imprint: | Providence, RI : American Mathematical Society, [2020] |
| Description: | v, 131 pages : illustrations ; 26 cm |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society, 0065-9266 ; number 1295 Memoirs of the American Mathematical Society ; no. 1295. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/12617470 |
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| 100 | 1 | |a Berger, Lisa, |d 1969- |e author. |0 http://id.loc.gov/authorities/names/no2020102328 |1 http://viaf.org/viaf/26159939437925251439 | |
| 245 | 1 | 0 | |a Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields / |c Lisa Berger, Chris Hall, Rene Pannekoek, Jennifer Park, Rachel Pries, Shahed Sharif, Alice Silverberg, Douglas Ulmer. |
| 264 | 1 | |a Providence, RI : |b American Mathematical Society, |c [2020] | |
| 300 | |a v, 131 pages : |b illustrations ; |c 26 cm | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
| 337 | |a unmediated |b n |2 rdamedia |0 http://id.loc.gov/vocabulary/mediaTypes/n | ||
| 338 | |a volume |b nc |2 rdacarrier |0 http://id.loc.gov/vocabulary/carriers/nc | ||
| 490 | 1 | |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. | |
| 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. | ||
| 650 | 0 | |a Curves, Algebraic. |0 http://id.loc.gov/authorities/subjects/sh85034916 | |
| 650 | 0 | |a Abelian varieties. |0 http://id.loc.gov/authorities/subjects/sh85000130 | |
| 650 | 0 | |a Jacobians. |0 http://id.loc.gov/authorities/subjects/sh85069214 | |
| 650 | 0 | |a Birch-Swinnerton-Dyer conjecture. |0 http://id.loc.gov/authorities/subjects/sh94001868 | |
| 650 | 0 | |a Rational points (Geometry) |0 http://id.loc.gov/authorities/subjects/sh2001008362 | |
| 650 | 0 | |a Legendre's functions. |0 http://id.loc.gov/authorities/subjects/sh85075778 | |
| 650 | 0 | |a Finite fields (Algebra) |0 http://id.loc.gov/authorities/subjects/sh85048351 | |
| 650 | 7 | |a Abelian varieties |2 fast |0 (OCoLC)fst00794347 | |
| 650 | 7 | |a Birch-Swinnerton-Dyer conjecture |2 fast |0 (OCoLC)fst00832903 | |
| 650 | 7 | |a Curves, Algebraic |2 fast |0 (OCoLC)fst00885451 | |
| 650 | 7 | |a Finite fields (Algebra) |2 fast |0 (OCoLC)fst00924905 | |
| 650 | 7 | |a Jacobians |2 fast |0 (OCoLC)fst00981033 | |
| 650 | 7 | |a Legendre's functions |2 fast |0 (OCoLC)fst00995590 | |
| 650 | 7 | |a Rational points (Geometry) |2 fast |0 (OCoLC)fst01090266 | |
| 700 | 1 | |a Hall, Chris, |d 1975- |e author. |0 http://id.loc.gov/authorities/names/no2003053312 |1 http://viaf.org/viaf/21832161 | |
| 700 | 1 | |a Pannekoek, René, |e author. |0 http://id.loc.gov/authorities/names/no2020102329 |1 http://viaf.org/viaf/305828410 | |
| 700 | 1 | |a Park, Jennifer Mun Young, |e author. |0 http://id.loc.gov/authorities/names/no2014105571 |1 http://viaf.org/viaf/310621852 | |
| 700 | 1 | |a Pries, Rachel, |d 1972- |e author. |0 http://id.loc.gov/authorities/names/no2020102330 |1 http://viaf.org/viaf/4252149844954502960007 | |
| 700 | 1 | |a Sharif, Shahed, |d 1977- |e author. |0 http://id.loc.gov/authorities/names/no2020102331 |1 http://viaf.org/viaf/38159939449525251675 | |
| 700 | 1 | |a Silverberg, Alice, |e author. |0 http://id.loc.gov/authorities/names/n85819986 |1 http://viaf.org/viaf/38384617 | |
| 700 | 1 | |a Ulmer, Douglas, |d 1960- |e author. |0 http://id.loc.gov/authorities/names/no2015046585 |1 http://viaf.org/viaf/315195219 | |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1295. | |
| 901 | |a Analytic | ||
| 903 | |a HeVa | ||
| 929 | |a cat | ||
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| 928 | |t Library of Congress classification |a QA1.A528 no.1295 |l ASR |c ASR-SciASR |i 12633493 | ||
| 927 | |t Library of Congress classification |a QA1.A528 no.1295 |l ASR |c ASR-SciASR |g Analytic |b A116851389 |i 10320399 | ||