Papers written by Dragos Ghioca

PhD thesis (Berkeley, May 2005). PDF

Publications

  1. The Mordell-Lang theorem for Drinfeld modules. Int. Math. Res. Not. IMRN, 2005, no. 53, 3273-3307. PDF
  2. Equidistribution for torsion points of a Drinfeld module. Math. Ann., 2006, vol. 336, no. 4, 841-865. PDF
  3. Division points on subvarieties of isotrivial semiabelian varieties. (with Rahim Moosa). Int. Math. Res. Not. IMRN, 2006, vol. 2006, Article ID 65437, 1-23. PDF
  4. The Lehmer inequality and the Mordell-Weil theorem for Drinfeld modules. J. Number Theory, 2007, vol. 122, no. 1, 37-68. PDF
  5. The local Lehmer inequality for Drinfeld modules. J. Number Theory, 2007, vol. 123, no. 2, 426-455. PDF
  6. The Tate-Voloch Conjecture for Drinfeld modules. J. Number Theory, 2007, vol. 125, no. 1, 85-94. PDF
  7. Siegel's Theorem for Drinfeld modules. (with Thomas J. Tucker). Math. Ann., 2007, vol. 339, no. 1, 37-60. PDF
  8. Mordell exceptional locus for subvarieties of the additive group. Math. Res. Lett., 2008, vol. 15, no. 1, 43-50. PDF
  9. Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture. (with Thomas J. Tucker and Michael E. Zieve). Invent. Math., 2008, vol. 171, no. 2, 463-483. PDF
  10. A dynamical version of the Mordell-Lang conjecture for the additive group. (with Thomas J. Tucker). Compositio Math., 2008, vol. 144, no. 2, 304-316. PDF
  11. The isotrivial case in the Mordell-Lang Theorem. Trans. Amer. Math. Soc., 2008, vol. 360, no. 7, 3839-3856. PDF
  12. Equidistribution and integral points for Drinfeld modules. (with Thomas J. Tucker). Trans. Amer. Math. Soc., 2008, vol. 360, no. 9, 4863-4887. PDF
  13. On permutation polynomials of prescribed shape. (with Amir Akbary and Qiang Wang). Finite Fields Appl., 2009, vol. 15, no. 2, 195-206. PDF
  14. Periodic points, linearizing maps, and the dynamical Mordell-Lang problem. (with Thomas J. Tucker). J. Number Theory, 2009, vol. 129, no. 6, 1392-1403. PDF
  15. Points of small height on varieties defined over a function field. Canad. Math. Bull., 2009, vol. 52, no. 2, 237-244. PDF
  16. Periods of orbits modulo primes. (with Amir Akbary). J. Number Theory, 2009, vol. 129, no. 11, 2831-2842. PDF
  17. Proof of a dynamical Bogomolov conjecture for lines under polynomial actions. (with Thomas J. Tucker). Proc. Amer. Math. Soc., 2010, vol. 138, no. 3, 937-942. PDF
  18. Elliptic curves over the perfect closure of a function field. Canad. Math. Bull., 2010, vol. 53, no. 1, 87-94. PDF
  19. Towards the full Mordell-Lang conjecture for Drinfeld modules. Canad. Math. Bull., 2010, vol. 53, no. 1, 95-101. PDF
  20. Reductions of points on elliptic curves. (with Amir Akbary and V. Kumar Murty). Math. Ann., 2010, vol. 347, no. 2, 365-394. PDF
  21. A gap principle for dynamics. (with Robert L. Benedetto, Par Kurlberg and Thomas J. Tucker). Compositio Math., 2010, vol. 146, no. 4, 1056-1072. PDF
  22. The dynamical Mordell-Lang problem for etale maps. (with Jason P. Bell and Thomas J. Tucker). Amer. J. Math., 2010, vol. 132, no. 6, 1655-1675. PDF
  23. On constructing permutations of finite fields. (with Amir Akbary and Qiang Wang). Finite Fields Appl., 2011, vol. 17, no. 1, 51-67. PDF
  24. Towards a dynamical Manin-Mumford conjecture. (with Thomas J. Tucker and Shou-Wu Zhang). Int. Math. Res. Not. IMRN, 2011, vol. 2011, no. 22, 5109-5122. PDF
  25. The Mordell-Lang question for endomorphisms of semiabelian varieties. (with Thomas J. Tucker and Michael E. Zieve). J. Theor. Nombres Bordeaux, 2011, vol. 23, no. 3, 645-666. PDF
  26. A case of the dynamical Mordell-Lang conjecture. (with Robert L. Benedetto, Par Kurlberg and Thomas J. Tucker, with an appendix by Umberto Zannier). Math. Ann., 2012, vol. 352, no. 1, 1-26. PDF
  27. A geometric variant of Titchmarsh Divisor problem. (with Amir Akbary). Internat. J. Number Theory, 2012, vol. 8, no.1, 53-69. PDF
  28. Linear relations between polynomial orbits. (with Thomas J. Tucker and Michael E. Zieve). Duke Math. J., 2012, vol. 161, no. 7, 1379-1410. PDF
  29. Periods of rational maps modulo primes. (with Robert L. Benedetto, Benjamin A. Hutz, Par Kurlberg, Thomas Scanlon and Thomas J. Tucker). Math. Ann., 2013, vol. 355, no. 2, 637-660. PDF
  30. Algebraic equations on the adelic closure of a Drinfeld module. (with Thomas Scanlon). Israel J. Math., 2013, vol. 194, no. 1, 461-483. PDF
  31. Preperiodic points for families of polynomials. (with Liang-Chung Hsia and Thomas J. Tucker). Algebra & Number Theory, 2013, vol. 7, no. 3, 701-732. PDF
  32. Unlikely, likely and impossible intersections without algebraic groups. (with Zoe Chatzidakis, David Masser and Guillaume Maurin). Rend. Lincei Mat. Appl., 2013, vol. 24, 485-501. PDF
  33. Variation of the canonical height in a family of rational maps. (with Myrto Mavraki). New York J. Math., 2013, vol. 19, 873-907. PDF
  34. Torsion points in families of Drinfeld modules. (with Liang-Chung Hsia). Acta Arith., 2013, vol. 161, no. 3, 219-240. PDF
  35. Integral points for Drinfeld modules. J. Number Theory, 2014, vol. 140, 93-121. PDF
  36. The Dynamical Mordell-Lang Conjecture. Canad. Math. Soc. Notes, 2014, vol. 46, no. 3, 14-15. PDF
  37. A Bogomolov type statement for function fields. Bull. Inst. Math. Acad. Sinica, 2014, vol. 9, no. 4, 641-656. PDF
  38. Preperiodic points for families of rational maps. (with Liang-Chung Hsia and Thomas J. Tucker). Proc. London Math. Soc., 2015, vol. 110, 395-427. PDF
  39. Portraits of preperiodic points for rational maps. (with Khoa Nguyen and Thomas J. Tucker). Math. Proc. Cambridge Philos. Soc., 2015, vol. 159, no. 1, 165-186. PDF
  40. Applications of p-adic analysis for bounding periods of subvarieties under etale maps. (with Jason P. Bell and Thomas J. Tucker). Int. Math. Res. Not. IMRN, 2015, vol. 2015, 3576-3597. PDF
  41. Bounded Height Conjecture for function fields. (with David Masser and Umberto Zannier). New York J. Math., 2015, vol. 21, 837-846. PDF
  42. The Dynamical Mordell-Lang problem for Noetherian spaces. (with Jason P. Bell and Thomas J. Tucker). Funct. Approx. Comment. Math., 2015, vol. 53, no. 2, 313-328. PDF
  43. Dynamical Anomalous Subvarieties: Structure and Bounded Height Theorems. (with Khoa Nguyen). Adv. Math., 2016, vol. 288, 1433-1462. PDF
  44. The Dynamical Mordell-Lang Conjecture. (with Jason P. Bell and Thomas J. Tucker). Mathematical Surveys and Monographs, 2016, vol. 210, American Mathematical Society, Providence, RI, xiv+280 pp. PDF
  45. A case of the Dynamical Andre-Oort Conjecture. (with Holly Krieger and Khoa Nguyen). Int. Math. Res. Not. IMRN, 2016, vol. 2016, 738-758. PDF
  46. Unlikely intersection for two-parameter families of polynomials. (with Liang-Chung Hsia and Thomas J. Tucker). Int. Math. Res. Not. IMRN, 2016, vol. 2016, 7589-7618. PDF
  47. Density of orbits of endomorphisms of abelian varieties. (with Thomas Scanlon). Trans. Amer. Math. Soc., 2017, vol. 369, no. 1, 447-466. PDF
  48. Dynamics of split polynomial maps: uniform bounds for periods and applications. (with Khoa Nguyen). Int. Math. Res. Not. IMRN, 2017, vol. 2017, 213-231. PDF
  49. The Dynamical Andre-Oort Conjecture: unicritical polynomials. (with Holly Krieger, Khoa Nguyen, and Hexi Ye). Duke Math. J., 2017, vol. 166, no. 1, 1-25. PDF
  50. On a variant of the Ailon-Rudnick theorem in positive characteristic. (with Liang-Chung Hsia and Thomas J. Tucker). New York J. Math., 2017, vol. 23, 213-225. PDF
  51. On a dynamical version of a theorem of Rosenlicht. (with Jason P. Bell and Zinovy Reichstein). Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 2017, vol. 17, no. 1, 187-204. PDF
  52. On the Medvedev-Scanlon conjecture for minimal threefolds of non-negative Kodaira dimension. (with Jason P. Bell, Zinovy Reichstein, and Matthew Satriano). New York J. Math., 2017, vol. 23, 1185-1203. PDF
  53. Unlikely intersections in arithmetic dynamics. Canad. Math. Soc. Notes, 2017, vol. 49, no. 4, 12-13. PDF
  54. The orbit intersection problem for linear spaces and semiabelian varieties. (with Khoa Nguyen). Math. Res. Lett., 2017, vol. 24, no. 5, 1263-1283. PDF
  55. Simultaneously preperiodic points for families of polynomials in normal form. (with Liang-Chung Hsia and Khoa Nguyen). Proc. Amer. Math. Soc., 2018, vol. 146, no. 2, 733-741. PDF
  56. A variant of a theorem by Ailon-Rudnick for elliptic curves. (with Liang-Chung Hsia and Thomas J. Tucker). Pacific J. Math., 2018, vol. 295, no. 1, 1-15. PDF
  57. Squarefree doubly primitive divisors in dynamical sequences. (with Khoa Nguyen and Thomas J. Tucker). Math. Proc. Cambridge Philos. Soc., 2018, vol. 164, no. 3, 551-572. PDF
  58. The Dynamical Andre-Oort Conjecture for cubic polynomials. (with Hexi Ye). Int. Math. Res. Not. IMRN, 2018, vol. 2018, no. 8, 2447-2480. PDF
  59. Density of orbits of endomorphisms of commutative linear algebraic groups. (with Fei Hu). New York J. Math., 2018, vol. 24, 375-388. PDF
  60. The Dynamical Manin-Mumford and the Dynamical Bogomolov Conjecture for endomorphisms of (P^1)^n. (with Khoa Nguyen and Hexi Ye). Compositio Math., 2018, vol. 154, no. 7, 1441-1472. PDF
  61. Algebraic dynamics of skew-linear self-maps. (with Junyi Xie). Proc. Amer. Math. Soc., 2018, vol. 146, no. 10, 4369-4387. PDF
  62. A dynamical variant of the Pink-Zilber conjecture. (with Khoa Nguyen). Algebra & Number Theory, 2018, vol. 12, no. 7, 1749-1771. PDF
  63. The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for split rational maps. (with Khoa Nguyen and Hexi Ye). J. Eur. Math. Soc. (JEMS), 2019, vol. 21, no. 5, 1571-1594. PDF
  64. The dynamical Mordell-Lang conjecture in positive characteristic. Trans. Amer. Math. Soc., 2019, vol. 371, no. 2, 1151-1167. PDF
  65. Bounded height in families of dynamical systems. (with Laura DeMarco, Holly Krieger, Khoa Nguyen, Thomas J. Tucker and Hexi Ye). Int. Math. Res. Not. IMRN, 2019, vol. 2019, no. 8, 2453-2482. PDF
  66. Density of orbits of dominant regular self-maps of semiabelian varieties. (with Matthew Satriano). Trans. Amer. Math. Soc., 2019, vol. 371, no. 9, 6341-6358. PDF
  67. Periodic subvarieties of semiabelian varieties and annihilators of irreducible representations. (with Jason P. Bell). Adv. Math., 2019, vol. 349, 459-487. PDF
  68. Rationality of dynamical canonical height. (with Laura DeMarco). Ergodic Theory Dynam. Systems, 2019, vol. 39, no. 9, 2507-2540. PDF
  69. Bounding periods of subvarieties of (P^1)^n. (with Jason P. Bell and Thomas J. Tucker). Math. Res. Lett., 2019, vol. 26, no. 4, 949-971. PDF
  70. A variant of the Mordell-Lang conjecture. (with Fei Hu, Thomas Scanlon and Umberto Zannier). Math. Res. Lett., 2019, vol. 26, no. 5, 1383-1392. PDF
  71. A variant of the Siegel's theorem for Drinfeld modules. (with Simone Coccia). J. Number Theory, 2020, vol. 216, 142-156. PDF
  72. The Dynamical Mordell-Lang Conjecture for skew-linear self-maps. (with Junyi Xie, with an appendix by Michael Wibmer). Int. Math. Res. Not. IMRN, 2020, vol. 2020, no. 21, 7433-7453. PDF
  73. Finite index theorems for iterated Galois groups of unicritical polynomials. (with Andrew Bridy, John R. Doyle, Liang-Chung Hsia and Thomas J. Tucker). Trans. Amer. Math. Soc., 2021, vol. 374, no. 1, 733-752. PDF
  74. A reformulation of the Dynamical Manin-Mumford Conjecture. (with Thomas J. Tucker). Bull. Aust. Math. Soc., 2021, vol. 103, no. 1, 154-161. PDF
  75. The Dynamical Mordell-Lang Conjecture for endomorphisms of semiabelian varieties defined over fields of positive characteristic. (with Pietro Corvaja, Thomas Scanlon and Umberto Zannier). J. Inst. Math. Jussieu, 2021, vol. 20, no. 2, 669-698. PDF
  76. Dynamical uniform bounds for fibers and a gap conjecture. (with Jason P. Bell and Matthew Satriano). Int. Math. Res. Not. IMRN, 2021, vol. 2021, no. 10, 7932-7946. PDF
  77. A question for iterated Galois groups in arithmetic dynamics. (with Andrew Bridy, John R. Doyle, Liang-Chung Hsia and Thomas J. Tucker). Canad. Math. Bull., 2021, vol. 64, no. 2, 401-417. PDF
  78. Points of small height on affine varieties defined over function fields of finite transcendence degree. (with Dac-Nhan-Tam Nguyen). Bull. Aust. Math. Soc., 2021, vol. 103, no. 3, 418-427. PDF
  79. Zariski dense orbits for regular self-maps of tori in positive characteristic. (with Sina Saleh). New York J. Math., 2021, vol. 27, 1274-1304. PDF
  80. A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic. (with Alina Ostafe, Sina Saleh and Igor E. Shparlinski). Bull. Aust. Math. Soc., 2021, vol. 104, no. 3, 381-390. PDF
  81. Order of torsion for reduction of linearly independent points for a family of Drinfeld modules. (with Igor E. Shparlinski). J. Number Theory, 2022, vol. 233, 112-125. PDF
  82. A Bertini type theorem for pencils over finite fields. (with Shamil Asgarli). Finite Fields Appl., 2022, vol. 77, Paper No. 101936, 13 pp. PDF
  83. Higher arithmetic degrees of dominant rational self-maps. (with Nguyen-Bac Dang, Fei Hu, John Lesieutre and Matthew Satriano). Ann. Sc. Norm. Sup. Pisa Cl. Sci., 2022, vol. 23, 465-483. PDF
  84. Zariski dense orbits for regular self-maps on split semiabelian varieties. (with Sina Saleh). Canad. Math. Bull., 2022, vol. 65, no. 1, 116-122. PDF
  85. On sparsity of representations of polynomials as linear combinations of exponential functions. (with Alina Ostafe, Sina Saleh and Igor E. Shparlinski). J. Lond. Math. Soc. (2), 2022, vol. 105, no. 4, 2076-2103. PDF
  86. A fusion variant of the classical and dynamical Mordell-Lang conjectures in positive characteristic. (with Jason P. Bell). New York J. Math., 2022, vol. 28, 1623-1636. PDF
  87. Zariski dense orbits for endomorphisms of a power of the additive group scheme defined over finite fields. (with Sina Saleh). J. Number Theory, 2023, vol. 244, 1-23. PDF
  88. Smoothness in pencils of hypersurfaces over finite fields. (with Shamil Asgarli). Bull. Aust. Math. Soc., 2023, vol. 107, no. 1, 85-94. PDF
  89. Linear families of smooth hypersurfaces over finitely generated fields. (with Shamil Asgarli and Zinovy Reichstein). Finite Fields Appl., 2023, vol. 87, Paper No. 102169, 10 pp. PDF
  90. A conjecture strengthening the Zariski dense orbit problem for birational maps of dynamical degree one. (with Jason P. Bell). Canad. Math. Bull., 2023, vol. 66, no. 2, 477-491. PDF
  91. Existence of pencils with nonblocking hypersurfaces. (with Shamil Asgarli and Chi Hoi Yip). Finite Fields Appl., 2023, vol. 92, Paper No. 102283. PDF
  92. Zariski dense orbits for regular self-maps of split semiabelian varieties in positive characteristic. (with Sina Saleh). Math. Proc. Cambridge Philos. Soc., 2023, vol. 175, no. 3, 479-519. PDF
  93. Plane curves giving rise to blocking sets over finite fields. (with Shamil Asgarli and Chi Hoi Yip). Des. Codes Cryptogr., 2023, vol. 91, no. 11, 3643-3669. PDF
  94. Collision of orbits for a one-parameter family of Drinfeld modules. J. Number Theory, 2024, vol. 257, 320-340. PDF
  95. Most plane curves over finite fields are not blocking. (with Shamil Asgarli and Chi Hoi Yip). J. Combin. Theory Ser. A, 2024, vol. 204, Article 105871. PDF
  96. The Mordell-Lang conjecture for semiabelian varieties defined over fields of positive characteristic. (with She Yang). Bull. Aust. Math. Soc., 2024, vol. 109, no. 2, 254-264. PDF
  97. Intersections of orbits of self-maps with subgroups in semiabelian varieties. (with Jason P. Bell). Bull. Lond. Math. Soc., 2024, vol. 56, no. 2, 783-795. PDF
  98. Rational self-maps with a regular iterate on a semiabelian variety. (with Jason P. Bell and Zinovy Reichstein). J. Number Theory, 2024, vol. 260, 103-119. PDF
  99. Tangent-filling plane curves over finite fields. (with Shamil Asgarli). Bull. Aust. Math. Soc., 2024, vol. 109, no. 2, 301-315. PDF
  100. Plane-filling curves of small degree over finite fields. (with Shamil Asgarli). to appear in the Rocky Mountain Journal of Mathematics. PDF
  101. A Mordell-Lang type problem for GL_m. (with Jason P. Bell and Yifeng Huang). to appear in the Bulletin of the Australian Mathematical Society. PDF
  102. Linear system of hypersurfaces passing through a Galois orbit. (with Shamil Asgarli and Zinovy Reichstein). to appear in the Research in Number Theory. PDF
  103. The isotrivial case in the Mordell-Lang conjecture for semiabelian varieties defined over fields of positive characteristic. to appear in the Canadian Mathematical Bulletin. PDF
  104. Effective isotrivial Mordell-Lang in positive characteristic. (with Jason P. Bell and Rahim Moosa). submitted for publication. PDF
  105. Proportion of blocking curves in a pencil. (with Shamil Asgarli and Chi Hoi Yip). submitted for publication. PDF
  106. Specializations of iterated Galois groups of PCF rational functions. (with Robert L. Benedetto, Jamie Juul and Thomas J. Tucker). submitted for publication. PDF
  107. A non-abelian variant of the classical Mordell-Lang conjecture. (with Yifeng Huang). submitted for publication. PDF
  108. Simultaneously preperiodic points for a family of polynomials in positive characteristic. submitted for publication. PDF
  109. Linear system of geometrically irreducible plane cubics over finite fields. (with Shamil Asgarli). submitted for publication. PDF
  110. Intersection of orbits for polynomials in characteristic p. (with Simone Coccia, Jungin Lee, and GyeongHyeon Nam). submitted for publication. PDF