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Algebraic Geometry

Arithmetic and Diophantine Geometry

14Gxx

[1] Kontogeorgis Aristides and Victor Rotger. On abelian automorphism groups of Mumford curves and applications to Shimura curves. arXiv:math.AG/0604099, 16 pages, 2006.
[2] Matthew H. Baker, Enrique González-Jiménez, Josep González, and Bjorn Poonen. Finiteness results for modular curves of genus at least 2. Amer. J. Math., 127(6):1325–1387, 2005.
[3] Tatiana Bandman, Gert-Martin Greuel, Fritz Grunewald, Boris Kunyavskiĭ, Gerhard Pfister, and Eugene Plotkin. Identities for finite solvable groups and equations in finite simple groups. Compos. Math., 142(3):734–764, 2006.
[4] Arthur Baragar and Ronald van Luijk. K3 surfaces with Picard number three and canonical vector heights. Math. Comp., 76(259):1493–1498 (electronic), 2007.
[5] Nigel Boston. Reducing the Fontaine-Mazur conjecture to group theory. In Progress in Galois theory, volume 12 of Dev. Math., pages 39–50. Springer, New York, 2005.
[6] Friederike Brezing and Annegret Weng. Elliptic curves suitable for pairing based cryptography. Des. Codes Cryptogr., 37(1):133–141, 2005.
[7] Ezra Brown, Bruce T. Myers, and Jerome A. Solinas. Hyperelliptic curves with compact parameters. Des. Codes Cryptogr., 36(3):245–261, 2005.
[8] Nils Bruin. Visualising Sha[2] in abelian surfaces. Math. Comp., 73(247):1459–1476 (electronic), 2004.
[9] Nils Bruin, E. Victor Flynn, Josep González, and Victor Rotger. On finiteness conjectures for modular quaternion algebras. arXiv:math.NT/0312443 v2, 25 pages, 2005.
[10] Jan Denef and Frederik Vercauteren. An extension of Kedlaya's algorithm to Artin-Schreier curves in characteristic 2. In Algorithmic Number Theory (Sydney, 2002), volume 2369 of Lecture Notes in Comput. Sci., pages 308–323. Springer, Berlin, 2002.
[11] Claus Diem. The GHS attack in odd characteristic. J. Ramanujan Math. Soc., 18(1):1–32, 2003.
[12] E. V. Flynn. The Hasse principle and the Brauer-Manin obstruction for curves. Manuscripta Math., 115(4):437–466, 2004.
[13] Steven D. Galbraith. Supersingular curves in cryptography. In Advances in Cryptology—Asiacrypt 2001 (Gold Coast), volume 2248 of Lecture Notes in Comput. Sci., pages 495–513. Springer, Berlin, 2001.
[14] Steven D. Galbraith. Weil descent of Jacobians. Discrete Appl. Math., 128(1):165–180, 2003.
[15] Steven D. Galbraith, Florian Hess, and Nigel P. Smart. Extending the GHS Weil descent attack. In Advances in Cryptology—Eurocrypt 2002 (Amsterdam), volume 2332 of Lecture Notes in Comput. Sci., pages 29–44. Springer, Berlin, 2002.
[16] P. Gaudry, F. Hess, and N. P. Smart. Constructive and destructive facets of Weil descent on elliptic curves. J. Cryptology, 15(1):19–46, 2002.
[17] Pierrick Gaudry. An algorithm for solving the discrete log problem on hyperelliptic curves. In Advances in Cryptology—Eurocrypt 2000 (Bruges), volume 1807 of Lecture Notes in Comput. Sci., pages 19–34. Springer, Berlin, 2000.
[18] Josep González and Victor Rotger. Non-elliptic Shimura curves of genus one. Journal Math. Soc. Japan, 58(4):927–948, 2006.
[19] Johan P. Hansen. Toric varieties, Hirzebruch surfaces and error-correcting codes. Appl. Algebra Engrg. Comm. Comput., 13(4):289–300, 2002.
[20] F. Hess. Weil descent attacks. In Advances in Elliptic Curve Cryptography, volume 317 of London Math. Soc. Lecture Note Ser., pages 151–180. Cambridge Univ. Press, Cambridge, 2005.
[21] Florian Hess. A note on the Tate pairing of curves over finite fields. Arch. Math. (Basel), 82(1):28–32, 2004.
[22] E. W. Howe and K. E. Lauter. Improved upper bounds for the number of points on curves over finite fields. Ann. Inst. Fourier (Grenoble), 53(6):1677–1737, 2003.
[23] Everett W. Howe. Supersingular genus-two curves over fields of characteristic three. arXiv:math.NT/0604413, 20 pages, 2006.
[24] Everett W. Howe, Kristin E. Lauter, and Jaap Top. Pointless curves of genus three and four. In Arithmetic, Geometry and Coding Theory (AGCT 2003), volume 11 of Sémin. Congr., pages 125–141. Soc. Math. France, Paris, 2005.
[25] Farzali A. Izadi and V. Kumar Murty. Counting points on an abelian variety over a finite field. In Progress in Cryptology—Indocrypt 2003, volume 2904 of Lecture Notes in Comput. Sci., pages 323–333. Springer, Berlin, 2003.
[26] Rafe Jones and Jeremy Rouse. Iterated endomorphisms of Abelian algebraic groups. arXiv:0707.2384, 34 pages, 2007.
[27] Kiran S. Kedlaya. Computing zeta functions via p-adic cohomology. In Algorithmic Number Theory, volume 3076 of Lecture Notes in Comput. Sci., pages 1–17. Springer, Berlin, 2004.
[28] Kenji Koike and Annegret Weng. Construction of CM Picard curves. Math. Comp., 74(249):499–518 (electronic), 2005.
[29] Andrew Kresch and Yuri Tschinkel. Integral points on punctured abelian surfaces. In Algorithmic Number Theory (Sydney, 2002), volume 2369 of Lecture Notes in Comput. Sci., pages 198–204. Springer, Berlin, 2002.
[30] Andrew Kresch and Yuri Tschinkel. On the arithmetic of del Pezzo surfaces of degree 2. Proc. London Math. Soc. (3), 89(3):545–569, 2004.
[31] Andrew Kresch and Yuri Tschinkel. Effectivity of Brauer-Manin obstructions. arXiv:math/0612665, 24 pages, 2007.
[32] L. Kulesz, G. Matera, and É. Schost. Uniform bounds on the number of rational points of a family of curves of genus 2. J. Number Theory, 108(2):241–267, 2004.
[33] Alan G. B. Lauder. Counting solutions to equations in many variables over finite fields. Found. Comput. Math., 4(3):221–267, 2004.
[34] Alan G. B. Lauder. A recursive method for computing zeta functions of varieties. LMS J. Comput. Math., 9:222–269 (electronic), 2006.
[35] F. Leprévost, M. Pohst, and A. Schöpp. Rational torsion of J0(N) for hyperelliptic modular curves and families of Jacobians of genus 2 and genus 3 curves with a rational point of order 5, 7 or 10. Abh. Math. Sem. Univ. Hamburg, 74:193–203, 2004.
[36] John Little and Hal Schenck. Toric surface codes and Minkowski sums. SIAM J. Discrete Math., 20(4):999–1014 (electronic), 2006.
[37] David Savitt. The maximum number of points on a curve of genus 4 over F8 is 25. Canad. J. Math., 55(2):331–352, 2003.
[38] Éric Schost. Computing parametric geometric resolutions. Appl. Algebra Engrg. Comm. Comput., 13(5):349–393, 2003.
[39] Edlyn Teske. An elliptic curve trapdoor system (extended abstract). In High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, volume 41 of Fields Inst. Commun., pages 341–352. Amer. Math. Soc., Providence, RI, 2004.
[40] Ronald van Luijk. Quartic K3 surfaces without nontrivial automorphisms. Math. Res. Lett., 13(2-3):423–439, 2006.
[41] Eric R. Verheul. Evidence that XTR is more secure than supersingular elliptic curve cryptosystems. J. Cryptology, 17(4):277–296, 2004.
[42] Gabor Wiese. Dihedral Galois representations and Katz modular forms. Doc. Math., 9:123–133 (electronic), 2004.

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