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Experimental Mathematics Volume 11, 2002 - Issue 3
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Original Articles

Abelian Surfaces over Finite Fields as Jacobians

Daniel Maisner Department de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona, Spain E-mail: danie1mQmat.uab.es
,
Enric Nart Departament de Matemàtiques Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona, Spain E-mail: nartQmat.uab.es
&
Everett W. Howe Center for Communications Research, 4320 Westerra Court, San Diego, CA, 92121-1967 E-mail: howeverQalumni.caltech.edu
Pages 321-337 | Published online: 03 Apr 2012

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Lenny Jones. (2022) When Does F(α) = F(α)?. The American Mathematical Monthly 129:1, pages 82-85.
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Travis Scholl. (2019) Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography. Experimental Mathematics 28:4, pages 385-397.
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Articles from other publishers (33)

Jonas Bergström, Valentijn Karemaker & Stefano Marseglia. (2023) Polarizations of Abelian Varieties Over Finite Fields via Canonical Liftings. International Mathematics Research Notices 2023:4, pages 3194-3248.
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Hanson Smith. (2022) Frobenius finds non-monogenic division fields of abelian varieties. International Journal of Number Theory 18:10, pages 2299-2315.
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WonTae Hwang & Keunyoung Jeong. (2022) Counting the number of the twists of certain polarized abelian varieties. Finite Fields and Their Applications 83, pages 102091.
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WonTae Hwang. (2022) Automorphism Groups of Simple Abelian Fourfolds over Finite Fields and Jordan Constants. Transformation Groups.
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Stefano Marseglia & Travis Scholl. (2021) Products and polarizations of super-isolated abelian varieties. Mathematische Zeitschrift 300:1, pages 445-462.
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LENNY JONES. (2021) CHARACTERISTIC POLYNOMIALS OF SIMPLE ORDINARY ABELIAN VARIETIES OVER FINITE FIELDS. Bulletin of the Australian Mathematical Society 104:3, pages 391-397.
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WonTae Hwang. (2021) On a classification of the automorphism groups of polarized abelian surfaces over finite fields. Finite Fields and Their Applications 72, pages 101809.
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WonTae Hwang & Kyunghwan Song. (2021) Absolutely simple polarized abelian varieties of odd Sophie Germain prime dimension over finite fields with maximal automorphism groups. Journal of Number Theory 222, pages 262-277.
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Edgar Costa, Ravi Donepudi, Ravi Fernando, Valentijn Karemaker, Caleb Springer & Mckenzie West. 2021. Arithmetic Geometry, Number Theory, and Computation. Arithmetic Geometry, Number Theory, and Computation 259 276 .
Taylor Dupuy, Kiran Kedlaya, David Roe & Christelle Vincent. 2021. Arithmetic Geometry, Number Theory, and Computation. Arithmetic Geometry, Number Theory, and Computation 375 448 .
Travis Scholl. (2020) Super-isolated abelian varieties. Journal of Number Theory 206, pages 138-168.
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Stefano Marseglia. (2019) Computing abelian varieties over finite fields isogenous to a power. Research in Number Theory 5:4.
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Ricard Garra, Josep M. Miret, Jordi Pujolàs & Nicolas Thériault. (2019) The 2-adic valuation of the cardinality of Jacobians of genus 2 curves over quadratic towers of finite fields. Journal of Algebra and Its Applications 18:07, pages 1950135.
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Valentijn Karemaker & Rachel Pries. (2019) Fully maximal and fully minimal abelian varieties. Journal of Pure and Applied Algebra 223:7, pages 3031-3056.
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Daiki Hayashida. (2019) The characteristic polynomials of abelian varieties of higher dimension over finite fields. Journal of Number Theory 196, pages 205-222.
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Benjamin Wesolowski. (2019) Generating subgroups of ray class groups with small prime ideals. The Open Book Series 2:1, pages 461-478.
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Сергей Георгиевич Влэдуц, Sergei Georgievich Vladut, Дмитрий Юрьевич Ногин, Dmitrii Yur'evich Nogin, Михаил Анатольевич Цфасман & Michael Anatol'evich Tsfasman. (2018) Многообразия над конечными полями: количественная теорияVarieties over finite fields: quantitative theory. Успехи математических наук Uspekhi Matematicheskikh Nauk 73:2(440), pages 75-140.
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David Ayotte, Antonio Lei & Jean-Christophe Rondy-Turcotte. (2016) On the parity of supersingular Weil polynomials. Archiv der Mathematik 106:4, pages 345-353.
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Omran Ahmadi, Gary McGuire & Antonio Rojas-León. (2015) Decomposing Jacobians of curves over finite fields in the absence of algebraic structure. Journal of Number Theory 156, pages 414-431.
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Gary McGuire, Vijaykumar Singh & Alexey Zaytsev. (2014) Classification of characteristic polynomials of simple supersingular abelian varieties over finite fields. Functiones et Approximatio Commentarii Mathematici 51:2.
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Sergey Rybakov. (2014) Finite group subschemes of abelian varieties over finite fields. Finite Fields and Their Applications 29, pages 132-150.
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Mohamed Saïdi. (2012) The cuspidalisation of sections of arithmetic fundamental groups. Advances in Mathematics 230:4-6, pages 1931-1954.
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P.M. Gauthier & N. Tarkhanov. (2012) On the instability of the Riemann hypothesis for curves over finite fields. Journal of Approximation Theory 164:4, pages 504-515.
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Robert Dryło. 2012. Progress in Cryptology - INDOCRYPT 2012. Progress in Cryptology - INDOCRYPT 2012 431 453 .
David Mandell Freeman & Takakazu Satoh. (2011) Constructing pairing-friendly hyperelliptic curves using Weil restriction. Journal of Number Theory 131:5, pages 959-983.
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Laura Hitt O'Connor, Gary McGuire, Michael Naehrig & Marco Streng. (2011) A CM construction for curves of genus 2 with p-rank 1. Journal of Number Theory 131:5, pages 920-935.
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Safia Haloui. (2010) The characteristic polynomials of abelian varieties of dimensions 3 over finite fields. Journal of Number Theory 130:12, pages 2745-2752.
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Laura Hitt. (2009) Families of genus 2 curves with small embedding degree. Journal of Mathematical Cryptology 3:1.
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Enric Nart & Christophe Ritzenthaler. (2008) Jacobians in isogeny classes of supersingular abelian threefolds in characteristic 2. Finite Fields and Their Applications 14:3, pages 676-702.
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Christian Robenhagen Ravnshøj. 2008. Pairing-Based Cryptography – Pairing 2008. Pairing-Based Cryptography – Pairing 2008 225 242 .
Daniel Maisner & Enric Nart. (2018) Zeta Functions of Supersingular Curves of Genus 2. Canadian Journal of Mathematics 59:2, pages 372-392.
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Gabriel Cardona & Enric Nart. 2007. Pairing-Based Cryptography – Pairing 2007. Pairing-Based Cryptography – Pairing 2007 132 151 .
Norman E. HurtNorman E. Hurt. 2003. Many Rational Points. Many Rational Points 317 344 .

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