Algebraic Geometry

Arithmetic and Diophantine Geometry

14Gxx

  1. 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 (2005), no. 6, 1325–1387.[MR]
  2. Edoardo Ballico, Antonio Cossidente, and Alessandro Siciliano, External flats to varieties in symmetric product spaces over finite fields, Finite Fields Appl. 9 (2003), no. 3, 300–309.[MR/doi]
  3. Tatiana Bandman, Gert-Martin Greuel, Fritz Grunewald, Boris Kunyavskii, Gerhard Pfister, and Eugene Plotkin, Identities for finite solvable groups and equations in finite simple groups, Compos. Math. 142 (2006), no. 3, 734–764.[MR]
  4. Arthur Baragar and Ronald van Luijk, K3 surfaces with Picard number three and canonical vector heights, Math. Comp. 76 (2007), no. 259, 1493–1498 (electronic).[MR]
  5. M. Borovoi, J. -L. Colliot-Thélène, and A. N. Skorobogatov, The elementary obstruction and homogeneous spaces, Duke Math. J. 141 (2008), no. 2, 321–364.[MR]
  6. Nigel Boston, Reducing the Fontaine-Mazur conjecture to group theory, Progress in Galois theory, Dev. Math., vol. 12, Springer, New York, 2005, pp. 39–50.[MR]
  7. Kristian Brander, An optimal unramified tower of function fields, Algebraic geometry and its applications, Ser. Number Theory Appl., vol. 5, World Sci. Publ., Hackensack, NJ, 2008, pp. 351–365.[MR/doi]
  8. R. de la Bret'che and T. D. Browning, Manin's conjecture for quartic del Pezzo surfaces with a conic fibration, preprint (2008).[arXiv]
  9. Friederike Brezing and Annegret Weng, Elliptic curves suitable for pairing based cryptography, Des. Codes Cryptogr. 37 (2005), no. 1, 133–141.[MR]
  10. Ezra Brown, Bruce T. Myers, and Jerome A. Solinas, Hyperelliptic curves with compact parameters, Des. Codes Cryptogr. 36 (2005), no. 3, 245–261.[MR]
  11. Nils Bruin, Visualising Sha[2] in abelian surfaces, Math. Comp. 73 (2004), no. 247, 1459–1476 (electronic).[MR]
  12. Jan H. Bruinier and Tonghai Yang, CM values of automorphic Green functions on orthogonal groups over totally real fields, preprint (2010), 50 pages.[arXiv]
  13. Patrick Corn, Tate-Shafarevich groups and K3 surfaces, Math. Comp., to appear (2007), 17 pages.
  14. Patrick Corn, The Brauer-Manin obstruction on del Pezzo surfaces of degree 2, Proc. Lond. Math. Soc. (3) 95 (2007), no. 3, 735–777.[MR]
  15. Jan Denef and Frederik Vercauteren, An extension of Kedlaya's algorithm to Artin-Schreier curves in characteristic 2, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 308–323.[MR]
  16. Xander Faber and Benjamin Hutz, On the number of rational iterated pre-images of the origin under quadratic dynamical systems, preprint (2008), 18 pages.[arXiv]
  17. Xander Faber, Benjamin Hutz, Patrick Ingram, Rafe Jones, Michelle Manes, Thomas J. Tucker, and Michael E. Zieve, Uniform bounds on pre-images under quadratic dynamical systems, Math. Res. Lett. 16 (2009), no. 1, 87–101.[MR/arXiv]
  18. Tom Fisher, A new approach to minimising binary quartics and ternary cubics, Math. Res. Lett. 14 (2007), no. 4, 597–613.[MR/link]
  19. Tom Fisher, Finding rational points on elliptic curves using 6-descent and 12-descent, J. Algebra 320 (2008), no. 2, 853–884.[MR]
  20. E. V. Flynn, The Hasse principle and the Brauer-Manin obstruction for curves, Manuscripta Math. 115 (2004), no. 4, 437–466.[MR]
  21. David Freeman and Kristin Lauter, Computing endomorphism rings of Jacobians of genus 2 curves over finite fields, Algebraic geometry and its applications, Ser. Number Theory Appl., vol. 5, World Sci. Publ., Hackensack, NJ, 2008, pp. 29–66.[MR]
  22. Steven D. Galbraith, Weil descent of Jacobians, Discrete Appl. Math. 128 (2003), no. 1, 165–180.[MR]
  23. Steven D. Galbraith and Xibin Lin, Computing pairings using x-coordinates only, Des. Codes Cryptogr. 50 (2009), no. 3, 305–324.[MR/eprint]
  24. Ralf Gerkmann, Relative rigid cohomology and deformation of hypersurfaces, Int. Math. Res. Pap. IMRP (2007), no. 1, Art. ID rpm003, 67.[MR]
  25. Josep González and Victor Rotger, Non-elliptic Shimura curves of genus one, J. Math. Soc. Japan 58 (2006), no. 4, 927–948.[MR]
  26. Cem Güneri, Henning Stichtenoth, and Ihsan Taşkın, Further improvements on the designed minimum distance of algebraic geometry codes, J. Pure Appl. Algebra 213 (2009), no. 1, 87–97.[MR]
  27. Johan P. Hansen, Toric varieties, Hirzebruch surfaces and error-correcting codes, Appl. Algebra Engrg. Comm. Comput. 13 (2002), no. 4, 289–300.[MR]
  28. David Harari and Tamás Szamuely, Galois sections for abelianized fundamental groups, Math. Ann. 344 (2009), no. 4, 779–800.[MR/arXiv]
  29. Florian Hess, A note on the Tate pairing of curves over finite fields, Arch. Math. (Basel) 82 (2004), no. 1, 28–32.[MR]
  30. Christopher Holden, Mod 4 Galois representations and elliptic curves, Proc. Amer. Math. Soc. 136 (2008), no. 1, 31–39 (electronic).[MR]
  31. David Holmes, Canonical heights on hyperelliptic curves and effective Q-factoriality for arithmetic surfaces, preprint (2010), 17 pages.[MR/arXiv]
  32. 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 (2003), no. 6, 1677–1737.[MR]
  33. Everett W. Howe, Supersingular genus-2 curves over fields of characteristic 3, Computational arithmetic geometry, Contemp. Math., vol. 463, Amer. Math. Soc., Providence, RI, 2008, pp. 49–69.[MR/arXiv]
  34. Everett W. Howe, Kristin E. Lauter, and Jaap Top, Pointless curves of genus three and four, Arithmetic, Geometry and Coding Theory (AGCT 2003), Sémin. Congr., vol. 11, Soc. Math. France, Paris, 2005, pp. 125–141.[MR]
  35. Nathan Owen Ilten and Hendrik Süß, AG codes from polyhedral divisors, preprint (2008), 30 pages.[arXiv]
  36. Farzali A. Izadi and V. Kumar Murty, Counting points on an abelian variety over a finite field, Progress in Cryptology—Indocrypt 2003, Lecture Notes in Comput. Sci., vol. 2904, Springer, Berlin, 2003, pp. 323–333.[MR]
  37. Rafe Jones and Jeremy Rouse, Iterated endomorphisms of abelian algebraic groups, Proc. London Math. Soc. 100 (2010), 763–794.[doi/arXiv]
  38. Samuel Kadziela, Rigid analytic uniformization of curves and the study of isogenies, Acta Appl. Math. 99 (2007), no. 2, 185–204.[MR]
  39. Kiran S. Kedlaya, Computing zeta functions via p-adic cohomology, Algorithmic Number Theory, Lecture Notes in Comput. Sci., vol. 3076, Springer, Berlin, 2004, pp. 1–17.[MR]
  40. Kenji Koike and Annegret Weng, Construction of CM Picard curves, Math. Comp. 74 (2005), no. 249, 499–518 (electronic).[MR]
  41. Aristides Kontogeorgis and Victor Rotger, On abelian automorphism groups of Mumford curves and applications to Shimura curves, preprint (2006), 16 pages.[arXiv]
  42. Andrew Kresch and Yuri Tschinkel, Integral points on punctured abelian surfaces, Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci., vol. 2369, Springer, Berlin, 2002, pp. 198–204.[MR]
  43. Andrew Kresch and Yuri Tschinkel, On the arithmetic of del Pezzo surfaces of degree 2, Proc. London Math. Soc. (3) 89 (2004), no. 3, 545–569.[MR]
  44. Andrew Kresch and Yuri Tschinkel, Effectivity of Brauer-Manin obstructions, Adv. Math. 218 (2008), no. 1, 1–27.[MR]
  45. 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 (2004), no. 2, 241–267.[MR]
  46. Gilles Lachaud and Christophe Ritzenthaler, On a conjecture of Serre on abelian threefolds, in Algebraic Geometry and its applications, Proceedings od the First SAGA conference, Papeete, France 2007, 2008, pp. 1–28.
  47. Alan G. B. Lauder, Counting solutions to equations in many variables over finite fields, Found. Comput. Math. 4 (2004), no. 3, 221–267.[MR]
  48. Alan G. B. Lauder, A recursive method for computing zeta functions of varieties, LMS J. Comput. Math. 9 (2006), 222–269 (electronic).[MR]
  49. 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 (2004), 193–203.[MR]
  50. John Little and Hal Schenck, Toric surface codes and Minkowski sums, SIAM J. Discrete Math. 20 (2006), no. 4, 999–1014 (electronic).[MR]
  51. Adam Logan, The Brauer-Manin obstruction on del Pezzo surfaces of degree 2 branched along a plane section of a Kummer surface, Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 3, 603–622.[MR]
  52. Ronald van Luijk, Quartic K3 surfaces without nontrivial automorphisms, Math. Res. Lett. 13 (2006), no. 2-3, 423–439.[MR/arXiv]
  53. Ronald van Luijk, Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces, preprint (2007), 17 pages.[arXiv]
  54. Michelle Manes, Q-rational cycles for degree-2 rational maps having an automorphism, Proc. Lond. Math. Soc. (3) 96 (2008), no. 3, 669–696.[MR]
  55. David Savitt, The maximum number of points on a curve of genus 4 over F8 is 25, Canad. J. Math. 55 (2003), no. 2, 331–352.[MR]
  56. Éric Schost, Computing parametric geometric resolutions, Appl. Algebra Engrg. Comm. Comput. 13 (2003), no. 5, 349–393.[MR]
  57. R. Shaw, The polynomial degrees of Grassmann and Segre varieties over GF(2), Discrete Math. 308 (2008), no. 5-6, 872–879.[MR]
  58. Edlyn Teske, An elliptic curve trapdoor system (extended abstract), High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, Fields Inst. Commun., vol. 41, Amer. Math. Soc., Providence, RI, 2004, pp. 341–352.[MR]
  59. Bianca Viray, A family of varieties with exactly one pointless rational fiber, preprint (2009), 4 pages.[arXiv]
  60. John Voight, Shimura curves of genus at most two, Math. Comp. 78 (2009), no. 266, 1155–1172.[MR]
  61. Gabor Wiese, Dihedral Galois representations and Katz modular forms, Doc. Math. 9 (2004), 123–133 (electronic).[MR]