• Thumbnail for Faltings's theorem
    Faltings's theorem is a result in arithmetic geometry, according to which a curve of genus greater than 1 over the field Q {\displaystyle \mathbb {Q} }...
    12 KB (1,310 words) - 22:56, 19 September 2024
  • In arithmetic geometry, Faltings' product theorem gives sufficient conditions for a subvariety of a product of projective spaces to be a product of varieties...
    2 KB (170 words) - 03:42, 16 November 2022
  • Thumbnail for Fermat's Last Theorem
    than two. This conjecture was proved in 1983 by Gerd Faltings, and is now known as Faltings's theorem. In the latter half of the 20th century, computational...
    103 KB (11,494 words) - 21:04, 20 September 2024
  • Thumbnail for Gerd Faltings
    Gerd Faltings (German pronunciation: [ɡɛʁt ˈfaltɪŋs] ; born 28 July 1954) is a German mathematician known for his work in arithmetic geometry. From 1972...
    7 KB (507 words) - 08:57, 13 September 2024
  • the equations. For g > 1 it was superseded by Faltings's theorem in 1983. In 1926, Siegel proved the theorem effectively in the special case g = 1 {\displaystyle...
    3 KB (361 words) - 13:03, 13 June 2024
  • {\displaystyle C} with A ( K ) {\displaystyle A(K)} be infinite? Because of Faltings's theorem, this is false unless C = A {\displaystyle C=A} . In the same context...
    5 KB (629 words) - 22:01, 24 February 2024
  • geometry) Extreme value theorem (calculus) F. and M. Riesz theorem (measure theory) FWL theorem (economics) Faltings's theorem (Diophantine geometry)...
    73 KB (6,015 words) - 12:17, 2 August 2024
  • Thumbnail for Wiles's proof of Fermat's Last Theorem
    Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be...
    58 KB (5,820 words) - 20:36, 7 September 2024
  • theorems in Diophantine geometry that are of fundamental importance include: Mordell–Weil theorem Roth's theorem Siegel's theorem Faltings's theorem Serge...
    8 KB (935 words) - 19:55, 6 May 2024
  • heights in Arakelov theory. In 1983, Faltings developed his theory of Faltings heights in his proof of Faltings's theorem. Classical or naive height is defined...
    17 KB (1,908 words) - 05:07, 24 June 2024