Timeline of abelian varieties

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This is a timeline of the theory of abelian varieties in algebraic geometry, including elliptic curves.

Early history[edit]

Seventeenth century[edit]

Eighteenth century[edit]

Nineteenth century[edit]

Twentieth century[edit]

Twenty-first century[edit]

Notes[edit]

  1. ^ PDF
  2. ^ Miscellaneous Diophantine Equations at MathPages[unreliable source?]
  3. ^ Fagnano_Giulio biography
  4. ^ E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (fourth edition 1937), p. 72.
  5. ^ André Weil, Number Theory: An approach through history (1984), p. 1.
  6. ^ Landen biography
  7. ^ Chronology of the Life of Carl F. Gauss
  8. ^ Semen Grigorʹevich Gindikin, Tales of Physicists and Mathematicians (1988 translation), p. 143.
  9. ^ Dale Husemoller, Elliptic Curves.
  10. ^ Richelot, Essai sur une méthode générale pour déterminer les valeurs des intégrales ultra-elliptiques, fondée sur des transformations remarquables de ces transcendantes, C. R. Acad. Sci. Paris. 2 (1836), 622-627; De transformatione integralium Abelianorum primi ordinis commentatio, J. Reine Angew. Math. 16 (1837), 221-341.
  11. ^ Gopel biography
  12. ^ http://www.gap-system.org/~history/Biographies/Rosenhain.html
  13. ^ Theorie der Abel'schen Funktionen, J. Reine Angew. Math. 54 (1857), 115-180
  14. ^ http://www.gap-system.org/~history/Biographies/Thomae.html
  15. ^ Robert Langlands, Some Contemporary Problems with Origins in the Jugendtraum
  16. ^ Über die Reduction einer bestimmten Klasse Abel'scher Integrale Ranges auf elliptische Integrale, Acta Math. 4, 392–414 (1884).
  17. ^ PDF, p. 168.
  18. ^ Ruggiero Torelli, Sulle varietà di Jacobi, Rend. della R. Acc. Nazionale dei Lincei , (5), 22, 1913, 98–103.
  19. ^ G. Scorza, Intorno alla teoria generale delle matrici di Riemann e ad alcune sue applicazioni,Rend. del Circolo Mat. di Palermo 41 (1916)
  20. ^ C. L. Siegel, Einführung in die Theorie der Modulfunktionen n-ten Grades, Math. Ann. 116 (1939), 617–657
  21. ^ Jean-Pierre Serre and John Tate, Good Reduction of Abelian Varieties, The Annals of Mathematics, Second Series, Vol. 88, No. 3 (Nov., 1968), pp. 492–517.
  22. ^ Daniel Huybrechts, Fourier–Mukai transforms in algebraic geometry (2006), Ch. 9.
  23. ^ J.-M. Fontaine, Il n'y a pas de variété abélienne sur Z, Invent. Math. (1985) no. 3, 515–538.