Computing Torsion Points on Curves

REFERENCES

• Baker , M. H. 2000 . “Torsion points on modular curves” . Invent Math. , 140 ( 3 ) : 487 – 509 . [Baker 2000]
   Web of Science ®Google Scholar
• Bosch , S. , Lütkebohmert , W. and Raynaud , M. 1990 . Néron models Berlin : Springer. . [Bosch et al. 1990], Ergebnisse der Mathematik (3) 21
   Google Scholar
• Boxall , J. and Grant , D. 2000 . “Examples of torsion points on genus two curves” . Trans. Amer. Math. Soc. , 352 ( 10 ) : 4533 – 4555 . [Boxall and Grant 2000]
   Web of Science ®Google Scholar
• Buium , A. 1996 . “Geometry of p-jets” . Duke Math. J. , 82 ( 2 ) : 349 – 367 . [Buium 1996]
   Web of Science ®Google Scholar
• Cassels , J. W. S. and Flynn , E. V. 1996 . Prolegomena to a middlebrow arithmetic of curves of genus 2 Cambridge : Cambridge Univ. Press. . [Cassels and Flynn 1996], London Math. Soc. Lecture Note Series 230
   Google Scholar
• Coleman , R. F. 1985 . “Torsion points on curves and p-adic abelian integrals” . Ann. of Math. (2) , 121 ( 1 ) : 111 – 168 . [Coleman 1985]
   Web of Science ®Google Scholar
• Coleman , R. F. 1986 . “Torsion points on Fermat curves” . Compositio Math. , 58 ( 2 ) : 191 – 208 . [Coleman 1986]
   Web of Science ®Google Scholar
• Coleman , R. F. 1987 . “Ramified torsion points on curves” . Duke Math. J. , 54 ( 2 ) : 615 – 640 . [Coleman 1987]
   Web of Science ®Google Scholar
• Coleman , R. F. 1989 . “Torsion points on abelian étale coverings of P1-(0,1,∞)” . Trans. A mer. Math. Soc. , 311 ( 1 ) : 185 – 208 . [Coleman 1989]
   Web of Science ®Google Scholar
• Coleman , R. F. , Tamagawa , A. and Tzermias , P. 1998 . “The cuspidal torsion packet on the Fermat curve” . J. Reine Angew. Math. , 496 : 73 – 81 . [Coleman et al. 1998]
   Web of Science ®Google Scholar
• Coleman , R. , Kaskel , B. and Ribet , K. A. 1999 . “Torsion points on X 0(N)”. ” . In Automorphic forms, automorphic representations, and arithmetic (Fort Worth, TX, 1996) vol. 1 , 27 – 49 . Providence , RI : Amer. Math. Soc. . [Coleman et al. 1999], Proc. Sym-pos. Pure Math. 66
   Google Scholar
• Drinfel'd , V. G. 1973 . “Two theorems on modular curves” . Funkcional. Anal, i Priložen. , 7 ( 2 ) : 83 – 84 . [Drinfel'd 1973], In Russian; translation in Functional Anal. Appl. 7 (1973), 155–156
   Google Scholar
• Elkik , R. 1990 . “Le théoréme de Manin-Drinfel'd”. ” . In Séminaire sur les pinceaux de courbes elliptiques (Paris, 1988) 59 – 67 . Paris : Soc. math. France. . [Elkik 1990], Astérisque 183
   Google Scholar
• Flynn , E. V. 1993 . “The group law on the Jacobian of a curve of genus 2” . J. Reine Angew. Math. , 439 : 45 – 69 . [Flynn 1993]
   Web of Science ®Google Scholar
• Goss , D. 1996 . Basic structures of function field arithmetic Berlin : Springer. . [Goss 1996], Ergebnisse der Mathematik (3) 35
   Google Scholar
• Greenberg , M. J. 1961 . “Schemata over local rings” . Ann. of Math. (2) , 73 : 624 – 648 . [Greenberg 1961]
   Web of Science ®Google Scholar
• Greenberg , M. J. 1963 . “Schemata over local rings, II” . Ann. of Math. (2) , 78 : 256 – 266 . [Greenberg 1963]
   Web of Science ®Google Scholar
• Hasegawa , Y. 1995 . “Table of quotient curves of modular curves X 0(N) with genus 2” . Proc. Japan Acad. Ser. A Math. Sci. , 71 ( 10 ) : 235 – 239 . [Hasegawa 1995]
   Google Scholar
• Hindry , M. 1988 . “Autour d'une conjecture de Serge Lang” . Invent. Math. , 94 ( 3 ) : 575 – 603 . [Hindry 1988]
   Web of Science ®Google Scholar
• Howe , E. W. , Leprévost , F. and Poonen , B. 2000 . “Large torsion subgroups of split Jacobians of curves of genus two or three” . Forum Math. , 12 ( 3 ) : 315 – 364 . [Howe et al. 2000]
   Web of Science ®Google Scholar
• Hrushovski , E. “The Manin-Mumford conjecture and the model theory of difference fields” . Ann. Pure Appl. Logic. , [Hrushovski ≥ 2001], To appear
   Web of Science ®Google Scholar
• Ishii , N. and Momose , F. 1991 . “Hyperelliptic modular curves” . Tsukuba J. Math. , 15 ( 2 ) : 413 – 423 . [Ishii and Momose 1991]
   Google Scholar
• Katz , N. M. 1981 . “Galois properties of torsion points on abelian varieties” . Invent. Math. , 62 ( 3 ) : 481 – 502 . [Katz 1981]
   Web of Science ®Google Scholar
• Keller , W. and Kulesz , L. 1995 . “Courbes algébriques de genre 2 et 3 possédant de nombreux points rationnels” . C. R. Acad. Sci. Paris Sér. I Math. , 321 ( 11 ) : 1469 – 1472 . [Keller and Kulesz 1995]
   Google Scholar
• Kubert , D. S. and Lang , S. 1981 . Modular units New York : Springer. . [Kubert and Lang 1981], Grundlehren der Math. Wissenschaften 244
   Google Scholar
• Léprevost , F. 1993 . “Points rationnels de torsion de jacobiennes de certaines courbes de genre 2” . C. R. Acad. Sci. Paris Sér. I Math. , 316 ( 8 ) : 819 – 821 . [Leprévost 1993]
   Google Scholar
• Manin , J. I. 1972 . “Parabolic points and zeta functions of modular curves” . Izv. Akad. Nauk SSSR Ser. Mat. , 36 : 19 – 66 . [Manin 1972], In Russian; translated in Math. USSR Izv. 6 (1972), 19–64
   Google Scholar
• Milne , J. S. 1986 . “Jacobian varieties”. ” . In Arithmetic geometry (Storrs, CT, 1984) Edited by: Cornell , G. and Silverman , J. H. 167 – 212 . New York : Springer. . [Milne 1986]
   Google Scholar
• Ogg , A. P. 1974 . “Hyperelliptic modular curves” . Bull. Soc. Math. Prance , 102 : 449 – 462 . [Ogg 1974]
   Web of Science ®Google Scholar
• Poonen , B. 1999 . “Mordell–Lang plus Bogomolov” . Invent. Math. , 137 ( 2 ) : 413 – 425 . [Poonen 1999]
   Web of Science ®Google Scholar
• Poonen , B. 2000 . “Genus-two curves with 22 torsion points” . C. R. Acad. Sci. Paris Sér. I Math. , 330 ( 7 ) : 573 – 576 . [Poonen 2000]
   Google Scholar
• Raynaud , M. 1983 . “Courbes sur une variété abélienne et points de torsion” . Invent. Math. , 71 ( 1 ) : 207 – 233 . [Raynaud 1983]
   Google Scholar
• Ribet , K. A. May 1999 . “Almost rational torsion points” May , Lectures at the University of Arizona. . [Ribet 1999]
   Google Scholar
• Szpiro , L. , Ullmo , E. and Zhang , S. 1997 . “Équirépartition des petits points” . Invent. Math. , 127 ( 2 ) : 337 – 347 . [Szpiro et al. 1997]
   Google Scholar
• Tamagawa , A. 2001 . “Ramification of torsion points on curves with ordinary semistable Jacobian varieties” . Duke Math. J. , 106 ( 2 ) : 281 – 319 . [Tamagawa 2001]
   Web of Science ®Google Scholar
• Tzermias , P. 2000 . “The Manin-Mumford conjecture: a brief survey” . Bull. London Math. Soc. , 32 ( 6 ) : 641 – 652 . [Tzermias 2000]
   Google Scholar
• Ullmo , E. 1998 . “Positivité et discrétion des points algébriques des courbes” . Ann. of Math. (2) , 147 ( 1 ) : 167 – 179 . [Ullmo 1998]
   Google Scholar
• Voloch , J. F. 1997 . “Torsion points on y² = x⁶ + 1” [Voloch 1997], http://www.ma.utexas.edu/users/voloch/preprint.htmlSee
   Google Scholar