Gerd Faltings

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Gerd Faltings (2005)

Gerd Faltings (born July 28, 1954 in Gelsenkirchen ) is a German mathematician and recipient of the Fields Medal . He is director at the Max Planck Institute for Mathematics and mainly deals with Diophantine equations , modular spaces and p-adic Galois representations .


Faltings grew up in a science-oriented family. His father was a physicist, his mother a chemist. Even as a schoolboy he stood out for his top mathematical achievements and won twice in the national mathematics competition .

After studying mathematics and physics at the Westphalian Wilhelms University in Münster (1972-1978), graduate and doctorate at Hans-Joachim Nastold to Dr. rer. nat. (1978) with his work On Macaulayfication , he went to Harvard University for a year with a grant from the German Research Foundation and completed his habilitation in 1981 in Münster .

In 1982 he moved to the University of Wuppertal and at the age of 27 became the youngest full professor of mathematics in Germany at the time .

In 1983 Faltings caused a sensation in the mathematical world with a 17-page paper on algebraic curves . In this work entitled Finiteness Theorems for Abelian Varieties on Number Fields , he proved at the age of only 27 that on algebraic curves over number fields of gender greater than 2 there can only be a finite number of points with rational coordinates , a conjecture of the British mathematician Louis Mordell - the so-called Mordell presumption  - from 1922, which was therefore unexplained for 60 years. In this work he also proves the Tate and Shafarevich conjectures at the same time and uses the Arakelov geometry. In 1986 he was awarded the Fields Medal for this breakthrough in algebraic geometry - the highest award in mathematics and in public perception, often compared with a Nobel Prize in other disciplines. He was the first and, until the award in 2018 to Peter Scholze, the only German to receive the Fields Medal. He later gave a second proof of the Mordell conjecture using Faltings' product theorem, in which he proved an even more general conjecture, the Mordell-Lang conjecture. In addition, together with Gisbert Wüstholz , he gave a new proof of Roth's theorem for which Roth received the Fields Medal in 1958.

In 1985 Faltings went to the USA for a long time and did research and taught at Princeton University , but kept a visiting professorship in Wuppertal. This triggered a public debate about the attractiveness of Germany as a research location for young scientists.

In 1994 Faltings returned to Germany and became a Scientific Member at the Max Planck Institute for Mathematics in Bonn, where he also took on one of the management posts from 1995.

Faltings also made a significant contribution to the solution of the so-called Fermat Hypothesis by the British mathematician Andrew Wiles .

In addition to specialist literature, Faltings has also published a collection of essays that is understandable for non-mathematicians as an introduction to modern mathematics.

In 1992 Faltings was elected a member of the Leopoldina . In 1999 Faltings was elected to the North Rhine-Westphalian Academy of Sciences and Arts , and in 2014 to the Academia Europaea .

Faltings is widowed and has two daughters.


See also

Fonts (selection)

  • Faltings, Gisbert Wüstholz (Ed.): Rational points. Vieweg, 1984, doi: 10.1007 / 978-3-322-83918-3 .
  • Gerd Faltings: Finiteness theorems for Abelian varieties over number fields . In: Inventiones mathematicae . tape 73 , 1983, pp. 349-366 , doi : 10.1007 / BF01388432 ( digitized version [accessed on September 9, 2010]).
  • Gerd Faltings: The assumptions of Tate and Mordell . In: Annual report of the German Mathematicians Association . tape 86 , no. 1 , 1984, p. 1–13 ( PDF [accessed September 9, 2010]).
  • Faltings: Arakelov's theorem for abelian varieties , Inventiones Mathematicae, Volume 72, 1983, pp. 337-347
  • Faltings: Arithmetic compactification of the modular space of the Abelian varieties , Arbeitstagung Bonn 1984, Lecture Notes in Mathematics 1111, Springer 1985, pp. 321–383, doi: 10.1007 / BFb0084598 .
  • Faltings: Calculus on arithmetic surfaces , Annals of Mathematics, Volume 119, 1984, pp. 387-424, doi: 10.2307 / 2007043
  • Faltings: Hodge-Tate structures and modular forms , Mathematische Annalen, Volume 278, 1987, pp. 133-149
  • Faltings: p-adic Hodge theory , Journal of the American Mathematical Society, Volume 1, 1988, pp. 255-299, doi: 10.1090 / S0894-0347-1988-0924705-1
  • Faltings, Ching-Li Chai: Degeneration of abelian varieties , results of mathematics and their border areas , Springer 1990
  • Faltings: Diophantine Approximation on Abelian Varieties , Annals of Mathematics, Volume 133, 1991, pp. 549-576
  • Faltings: Lectures on the arithmetic Riemann-Roch theorem , Annals of Mathematical Studies 127, Princeton University Press 1992
  • Faltings, Gisbert Wüstholz : Diophantine approximations on projective spaces , Invent. Math., Volume 116, 1994, pp. 109-138, doi: 10.1007 / BF01231559 , online at DigiZeitschriften (freely accessible)
  • Faltings (Ed., Introduction): Modern Mathematics. Spectrum, Akademie Verlag (series intelligible research ), Heidelberg / Berlin / Oxford 1996, ISBN 3-8274-0025-2 .
  • Faltings: Almost étale extensions , Astérisque, No. 279, 2002, pp. 185-270.
  • Faltings: Diophantine Equations , in: Mathematics Unlimited, Springer 2001, pp. 449–454, doi: 10.1007 / 978-3-642-56478-9_21

Web links

Commons : Gerd Faltings  - Collection of images, videos and audio files

Individual evidence

  1. The corresponding theorem for integer points was already proven by Carl Ludwig Siegel in the 1920s . The version of the mordell presumption for functional bodies was proven by Yuri Manin and Hans Grauert in the 1960s. For number fields there has also been an alternative proof by Vojta since the late 1980s.
  2. Klaus Friedrich Roth and Alexander Grothendieck came from Germany, but had been expelled by the National Socialists and Wendelin Werner was a native German, but took on French citizenship early on.
  3. Member entry by Gerd Faltings (with picture and CV) at the German Academy of Natural Scientists Leopoldina , accessed on July 5, 2016.
  5. Prof. Dr. Gerd Faltings. Member entry at the Academy of Sciences in Göttingen , accessed on August 4, 2016 .
  6. Prime Minister Rüttgers presents the Order of Merit of the Federal Republic of Germany to 16 citizens: "Your commitment distinguishes us all". ( Memento from November 15, 2010 in the Internet Archive ). Press release. State Chancellery of North Rhine-Westphalia, June 18, 2009.
  7. ^ Heinz Gumin Prize for Mathematics from the Carl Friedrich von Siemens Foundation. On:
  8. ^ "Like a Nobel Prize Winner from Münster". On:
  9. ^ The Shaw Prize in Mathematical Sciences 2015 ...